In 2008, as California confronted its most severe fiscal crisis since the Great Depression, the center of power in the state capital was a tent. It was set up in the courtyard outside the office of Gov. Arnold Schwarzenegger, an invitation-only retreat with folding chairs, a fake grass floor and ashtrays. Mr. Schwarzenegger, his aides and California’s most influential players — mostly white men — went there to smoke expensive cigars and talk politics and legislative deals.

But not Karen Bass.

Newly elected as the speaker of the State Assembly, Ms. Bass felt apart from that club the moment she stepped through the canvas flaps at the invitation of Mr. Schwarzenegger, a Republican.

“‘I guess you probably don’t want to be doing business here,’” the governor told her, as Ms. Bass recalled in a recent interview. “He didn’t know what to do. And that was right. I didn’t want to be in the tent. “

Here she was, a liberal Democrat and the first Black woman to lead a statehouse in the nation’s history, one of the three most powerful elected leaders of California in a moment of fiscal peril, and a wholly different kind of player navigating among men in a thick haze of cigar smoke.

“They didn’t know what to make of me,” she said.

Today Ms. Bass, a 66-year-old congresswoman and head of the Congressional Black Caucus, is among the leading candidates being considered for vice president by Joseph R. Biden Jr. But in some ways she is still an outsider, making her way in an overwhelmingly male political culture epitomized 12 years ago by Mr. Schwarzenegger, the shoot-’em-up action movie star, and today by the power circles in Washington, where the presidency and vice presidency remain all-male redoubts. She is barely known to many Americans, even to many leading Democrats, who — like the men in that tent in Sacramento — are now trying to figure out what to make of her.

And of all the contenders under consideration, none offer quite the contrast with Mr. Biden — in the story of her life and the story of her politics — as the Democratic congresswoman from California.

Ms. Bass grew up in a Black middle-class neighborhood in central Los Angeles; Mr. Biden spent his first years in predominantly white, middle-class Scranton, Pa. Mr. Biden was elected to his first public office in 1970, when he was 27. Ms. Bass was 51 when she was first elected to the Assembly.

Ms. Bass was liberal in a state known as one of the most liberal in the nation. Mr. Biden is the face of the moderate wing of the Democratic Party. One of Ms. Bass’s earliest causes, when she was a community organizer confronting crime, drugs and poverty, was opposing the very criminal justice law that Mr. Biden had championed, with its mandatory jail terms.

At every step in her political career, Ms. Bass had to be coaxed to run for a higher office. Mr. Biden has been running for president for nearly half a century.

In many ways, Ms. Bass could help Mr. Biden against President Trump. She would make history as the first Black woman to become a major party’s candidate for vice president. She talks more about conciliation than confrontation and does not have as many detractors as some of her rivals, including Senator Elizabeth Warren of Massachusetts and Senator Kamala Harris of California.ImageMs. Bass with other House Democrats on Capitol Hill in June, before the vote for the George Floyd Justice in Policing Act. Credit…Anna Moneymaker for The New York Times

Ms. Bass’s advocacy of liberal positions on criminal justice, poverty, housing, foster care and welfare could provide a Biden-Bass ticket a lift with progressive and younger voters. She would arguably be the most liberal politician chosen for vice president since Jimmy Carter tapped Walter F. Mondale as his running mate in 1976.

But her record of espousing progressive causes, lack of experience as a national campaigner and still largely unexplored record in public life also offer targets for Mr. Trump.

In the 1970s, Ms. Bass joined the Venceremos Brigade, a group of young leftists working on construction projects in Fidel Castro’s Cuba. When Castro died in 2016, she put out a statement saying that “the passing of the Comandante en Jefe is a great loss to the people of Cuba.” Those positions could allow Mr. Trump to continue to attack the Democratic ticket as socialist, and could be damaging with many Cubans in Florida and moderate voters across the Midwest.

Ms. Bass said she had made a mistake calling Castro “Comandante en Jefe,” a description widely detested by Cuban exiles. “Wouldn’t do that again,” she said Sunday on NBC’s “Meet the Press.” “Talked immediately to my colleagues from Florida and realized that that was something that just shouldn’t have been said.”

She said she had gone to Cuba to help the Cuban people by building houses and later to recruit doctors for the United States. “Now, that doesn’t excuse the fact that I know the Castro regime has been a brutal regime to its people,” she said.

Chapters of her career that might have gone unnoticed, even as the leader of the Assembly or a prominent member of Congress, are now coming to the forefront with the scrutiny that comes with being a potential candidate for vice president.

In one example, Ms. Bass spoke effusively about the Church of Scientology, the organization scrutinized over cultlike practices and alleged abuse of members, at the opening of its world headquarters in Los Angeles in 2010. Over the weekend, she tweeted a statement explaining why she had attended (it was a big project in her district) and added, “Just so you all know, I proudly worship at First New Christian Fellowship Baptist Church in South LA.”

Back in her days as a street organizer, she had never thought about running for office — not for the Assembly, not for speaker and not for Congress.

And certainly not for vice president.

“Oh God, no!” she said. “There isn’t anything in my background that would make you think that I was planning to run for office, period.”

As Mr. Biden closes in on making his choice, Ms. Bass has become a classic inside player, calling party leaders, giving interviews and joining Mr. Biden for a virtual fund-raiser where, in a preview of sorts, she attacked Mr. Trump. Yet she never forgot the lessons she learned in those first days as Assembly speaker.

“When a woman is in a role that’s new, people underestimate,” she said. “You need to know that the minute I got the job, the question was, was I really going to last and be a speaker? Is she real, does she really have any power?”

‘I felt like I had failed a generation’

As she grew up in 1960s Los Angeles, Ms. Bass watched the civil rights movement unfold on the nightly news with her father, volunteering to walk precincts for Robert F. Kennedy, who was assassinated not far from her home.

After graduating from the physician assistant program at the University of Southern California, Ms. Bass worked in an emergency room and taught on the faculty of the college. As she saw more evidence of the crack epidemic that was starting to ravage what was then called South Central Los Angeles, she started a group called the Community Coalition for Substance Abuse Prevention and Treatment, with the help of a federal grant.ImageMs. Bass was the executive director of the Community Coalition in South Central Los Angeles, where she worked to close down businesses like liquor stores and replace them with schools and other businesses.Credit…Ken Hively/Los Angeles Times, via Getty Images

While elected officials were beginning to enact harsh legal punishments, Ms. Bass viewed addiction as a public health crisis — hardly a popular view at the time. In meetings in living rooms and community centers, Ms. Bass argued that there were responses to the epidemic other than the aggressive policing that was widespread in Los Angeles, such as curbing the number of liquor stores in the area. The Community Coalition would become one of the largest and most influential advocacy groups in the city.

“What she saw quickly was that this was not going to be a time-limited campaign to stop government from criminalizing people — she realized this was going on at a national level and set about to build an organization that was really going to be focused on local reality,” said Marqueece Harris-Dawson, who took over the organization from Ms. Bass and is now a councilman from the area.

What made her work notable, Mr. Harris-Dawson said, was her emphasis on bringing attention to local residents. When television cameras showed up, she would often step aside and defer to the people who lived there, her attitude shaped in part by seeing the civil rights movement lose momentum after the assassinations of the Rev. Dr. Martin Luther King Jr. and Robert Kennedy.

For young organizers on staff, she offered specific lessons: Talk to everyone you can meet in the community, don’t rely on rhetoric and theories learned in college or activist circles, always have the conversation with someone who has expressed disagreement with you. She instructed them to shop in local grocery stores and strike up conversations with residents while waiting in line.

At the time, South Los Angeles was starting to shift from being a largely African-American neighborhood to one where Latinos eventually became the majority. The neighborhood would soon go through turmoil after a video captured members of the Los Angeles Police Department beating Rodney King after a high-speed police chase in 1991.ImageSmoke rising from a shopping center burned by rioters in Los Angeles in 1992 after four police officers were acquitted in the beating of Rodney King.Credit…Paul Sakuma/Associated Press

Ms. Bass said she initially thought the widely seen recording of the beating would drive sweeping change — “finally, there was evidence of what we had been talking about for years,” she said. She, like many others in the city, was stunned when the officers were acquitted in 1992 and disheartened when the verdict was met with violence and riots, many in her neighborhood.

“I felt like I had failed a generation, that they were so angry and that we hadn’t gotten change,” she said.

In the weeks after the uprising, Ms. Bass went block by block surveying the damage, which had ravaged large areas of the city. As officials set about plans for rebuilding, she focused on keeping out the kinds of businesses that residents had long complained were too prevalent, such as liquor stores and motels, and which she said contributed to the proliferation of drugs in the community.

By 1994, there was clear evidence of how much the Community Coalition was going against the grain with its theories for dealing with crime. And it came from Washington: a crime bill that would set mandatory minimum sentences for possession of crack cocaine.

One of the main champions of the bill was Mr. Biden.

“The crime bill was aimed at the war on drugs, and that went against the very reason she started Community Coalition,” said Mark Ridley-Thomas, a Los Angeles County supervisor and longtime friend of Ms. Bass’s. “She knew that the declaration of a war on drugs was to declare war on human beings who were suffering from a range of addictions, and that was the wrong approach.”

Ms. Bass initially thought that she could be more effective dealing with the ills of her city — drugs, crime, poverty — in private organizations free of the strains of electoral politics.ImageMs. Bass with fellow activists in 1992. As she worked for the Community Coalition for Substance Abuse Prevention and Treatment, she began to attain local prominence. Credit…Community Coalition

But during those years in Los Angeles, Ms. Bass achieved a level of prominence and prestige in the community and with local officials, who began to consult her on issues like appointments to the Police Department and education policy.

Then, in 2004, pressed by elected officials whom she had been working with, she agreed to run for the State Assembly. The outside player was ready to move to the inside.

Crafting a way out of fiscal crisis

California was sliding into crisis — a $41 billion deficit, larger than the entire budget of many states — when Ms. Bass was elected speaker in early 2008. For the next two years, she and other legislative leaders struggled with Mr. Schwarzenegger over a punishing package of spending cuts and tax increases to rescue California from its worst fiscal crisis since the Depression.

It also was a time of a tragedy in her life: In 2006, her only daughter and her son-in-law were killed in a car crash, an echo of the loss Mr. Biden has experienced; his wife and daughter were killed in an automobile accident in 1972.

“I had a choice as to whether to go back to work or hide,” Ms. Bass said. “I had to embrace the grief and wrap myself in grief. People don’t know how to deal with death and people avoid you, people don’t know what to say. Parents who have lost their children, you join a club that you didn’t ask to be a part of.”

The collapse of the national economy and housing market had hammered the state’s finances. Workers were forced to take furloughs. Vendors were paid with i.o.u.s, and tax refunds were delayed.

“It was the worst budget time in the history of California by far,” said Michael C. Genest, who was Mr. Schwarzenegger’s top financial adviser. “The major dynamic was that Republicans wanted to cut, Democrats wanted to raise taxes. And the reality was we could never cut enough to balance the budget. And we could never raise taxes enough to balance the budget.”

Democrats held a substantial majority in the Assembly and the Senate. But passing a budget in California at the time required a vote by two-thirds of members of each chamber. As a result, Republican leaders had significant power in the negotiations.

John A. Pérez, who succeeded Ms. Bass as speaker, said the dynamic of a minority party holding the votes needed to pass legislation greatly complicated her negotiations with the Senate and governor.

“But then she had the hard work of delivering the votes in the caucus,” he said. “And nobody goes to office to make cuts on programs they hold near and dear.”

Antonio R. Villaraigosa, who was the mayor of Los Angeles at the time, said he had pushed her for speaker because he thought she had the political skills to navigate a particularly difficult time in Sacramento.

“I thought we needed a leader who could work across the aisles,” he said. “She’s unabashedly a progressive, but she’s also practical and she knows how to work with Republicans.”

It was during that period that she honed the political and legislative skill that have drawn the attention of Mr. Biden — the drive for consensus, a quiet if firm manner, an ability to work with people on the other side of the political spectrum.

“I would make the decisions and go tell everybody: OK, this is the decision we made,” said Fabian Núñez, who was speaker before Ms. Bass. “She was a coalition builder. She wanted the buy-in.”

To this day, Ms. Bass remembers the unlikely alliance with Mr. Schwarzenegger and how they navigated the budget crisis from vastly different ideological perspectives. She would joke morosely when it came time for the daily walk through the Capitol to Mr. Schwarzenegger’s office, past the clusters of reporters and lobbyists.

“She used to refer to our daily negotiations as going to Gitmo,”said Darrell Steinberg, who was the Democratic leader of the Senate at the time and is now the mayor of Sacramento. “‘Gotta go to Gitmo.’”ImageMr. Schwarzenegger talking with Ms. Bass at a budget meeting in his Capitol office in Sacramento in January 2009.Credit…Rich Pedroncelli/Associated Press

The budget deal agreed to in February 2009 forced sharp concessions from Democrats and Republicans: $14.8 billion in cuts from health care, education, public transit and other social services; $12.5 billion in tax increases;$5.4 billion in borrowing; and various accounting gimmicks, including reliance on an infusion of federal aid. And as the state economy kept deteriorating, and voters refused to approve some of the taxes, California was back in the red by spring, forcing Ms. Bass to support even more budget cuts.

“She was unflappable,” Mr. Steinberg said. “It was high-stress. And we were making decisions that we did not want to make. Deep cuts to things that we cherished.”

Ms. Bass found herself having to go against years of her advocacy by yielding to Mr. Schwarzenegger and Republicans on issues like foster care and welfare.

“It was very devastating personally,” she said. “The whole reason I wanted to run for office to begin with was to expand the social safety net.”

As Ms. Bass finds herself in contention for a position she had never sought or considered, a critical question has emerged: Is the ability to seek consensus versus confrontation, which has served her so well over the decades, what is required for a vice-presidential candidate in today’s brutal political environment?

The No. 2 person on the ticket is often expected to carry the burden of delivering searing attacks. Mr. Biden’s running mate is likely to face particular scrutiny from Mr. Trump, who has struggled to find an effective line of attack against the former vice president.

That said, Ms. Bass’s nonthreatening style and ability to make alliances could prove to be a tonic in Washington in a post-Trump era. She counts among her friends an old fellow legislator from Sacramento, Kevin McCarthy, the House minority leader and Trump ally.

“People use the word nice about her, if you notice,” Mr. Villaraigosa said. “But I think a better word is — she knows how to stand up for what she believes in, without being difficult.”

Ms. Bass said that she was glad to hear herself described as nice “as opposed to mean” and that with the nation reeling from an epidemic, confrontation politics seemed petty. But, she added, “Nice doesn’t mean I wouldn’t fight.”