LOS ANGELES — For months, Representative Karen Bass was the one to beat in the race to lead the nation’s second-largest city.

She had undergone a decades-long transformation from physician assistant to community organizer to powerful political leader. Fresh from President Biden’s short list for vice president, she was encouraged by supporters across Los Angeles to run for mayor.

Then came Rick Caruso, a billionaire mall mogul who joined the race on the last day possible, and a more than $35 million self-funded campaign blitz vowing to “clean up” the crime and homelessness that has gripped the city under the watch of liberal politicians, including Ms. Bass.

Now, the 68-year-old congresswoman faces a close fight for an office that experts say will determine the trajectory of a diverse, global city at a pivotal time.

A recent poll co-sponsored by the University of California, Berkeley, and the Los Angeles Times showed Ms. Bass and Mr. Caruso almost neck-and-neck, with the congresswoman slightly ahead. While a candidate can win the election outright by getting more than 50 percent of the primary vote, political experts say that is exceedingly unlikely to happen in Tuesday’s election.

Twelve candidates are on the ballot, though two city officials dropped out of the race last month, with one endorsing Mr. Caruso and the other endorsing Ms. Bass. City Councilman Kevin de León, the former State Senate leader, was a distant third in the poll.

Ms. Bass would be the first Black woman — and the first woman — to become the mayor of Los Angeles. The contest is nonpartisan, but she has the backing of much of the Democratic elite as well as many progressive community groups in the heavily Democratic city.

On Friday, Ms. Bass said she felt energized and excited in the final days of the primary campaign. And even though Mr. Caruso has dominated the airwaves — her campaign has spent a little more than $3 million total, roughly one-tenth of his expenditures — Ms. Bass said she wasn’t worried.

“I actually think the ads have driven attendance at events that I’ve had,” she said. “They feel bombarded.”

Mr. Caruso’s campaign has portrayed Los Angeles as a city in decay, where crime has spun out of control and homeless encampments have blighted the landscape. Police, he has told supporters, have been “handcuffed” by criminal justice reform movements.

A former Republican who re-registered as a Democrat less than a month before entering the race, Mr. Caruso has vowed to quickly address homelessness and crime by building temporary shelters and hiring 1,500 new police officers — plans that his critics say will be impossible to enact given factors including the limitations of the mayor’s office, which shares governmental power with a number of other institutions.

Ms. Bass’s campaign has sought to address with urgency the fear and anger animating many voters while acknowledging that fixing the city’s deeply rooted problems will take systemic change — and, crucially, time. She has highlighted her connections to the state and federal governments and has said she would leverage those ties to bring more aid to help move people off the streets.

“You can come at this in a superficial way,” Ms. Bass said of addressing homelessness. “That is not going to address the problem unless we align all of the resources that this country has to offer and certainly that our city has to offer.”

She has also drawn the ire of some on the left for not only rejecting calls to defund the Los Angeles Police Department but proposing to put up to 250 additional officers on the street.

“If our movement does not have an answer for people who are concerned about crime,” she said, “we are essentially handing it over to conservatives.”

Ms. Bass’s supporters say that pragmatism and her ability to build coalitions around often-complex policy plans make her well-suited to lead a government where power is diffuse by design.

Mike Bonin, a City Council member who represents a district that includes both Mr. Caruso’s home and one of his shopping centers, said that he likes Mr. Caruso personally. But he said he was supporting Ms. Bass.

“She and I share the same values about what government should be doing to help people and share the same perspective that it’s vitally important to address the structural root causes of problems, even when that doesn’t have immediate political payoff,” he said. “I think L.A. is at a really challenging, perilous time and that’s exactly the kind of leadership that we need.”