GEOFF BENNETT: More than 730,000 New Yorkers have already cast ballots ahead of tomorrow's mayoral election, more than four times the number that voted early four years ago.

It's a race with big stakes for the city and beyond.

Democratic socialist Zohran Mamdani has vaulted from a relatively unknown state legislator to the front-runner to lead the largest city in the country.

William Brangham reports on what his potential victory means for New York City and the larger Democratic Party.

(CHANTING) WILLIAM BRANGHAM: At a packed concert venue in Queens recently, thousands of supporters gave Zohran Mamdani the rock star treatment.

Mamdani joked about just how unlikely his meteoric rise was.

ZOHRAN MAMDANI (D), New York City Mayoral Candidate: As recently as this February, our support had reached the eye-watering heights of 1 percent.

(CHEERING) ZOHRAN MAMDANI: We were tied with noted candidate "Someone Else."

(LAUGHTER) WILLIAM BRANGHAM: But, today, he is the front-runner to be New York's next mayor after winning a crowded Democratic primary with his charismatic, relentlessly on-message campaign about affordability.

ZOHRAN MAMDANI: No New Yorker should ever be priced out of anything they need to survive.

(CHEERING) WILLIAM BRANGHAM: His supporters are all in.

MORGAN PERRY, Mamdani Supporter: What is it going to be like in the future when we want to raise families, when we want to do whatever else?

And it's important that there's a groundwork for that, which currently right now is a little shaky.

ASHLEY HUFFORD, Mamdani Supporter: We want the city to be more affordable.

We want people to be fed.

We don't want ICE on the street.

Like, these are all things.

And I don't know if I trust another candidate to be able to do those things.

OWEN CROWLEY, Mamdani Supporter: It feels like change, and it feels like this is a hope for change for the better.

WILLIAM BRANGHAM: The 34-year-old Democratic socialist is leading most polls by double digits.

Republican Curtis Sliwa, founder of the volunteer vigilante group the Guardian Angels, and former New York Governor Andrew Cuomo are trailing.

FMR.

GOV.

ANDREW CUOMO (I-NY), NEW York City Mayoral Candidate: And the voters are going to have to decide in this election, what candidate has the plan to save the city and what candidate can get it done, not just talk about it?

WILLIAM BRANGHAM: Cuomo is running as an independent after his stunning loss in the Democratic primary this summer.

Mamdani beat him by more than 12 percent.

New York's current mayor, Eric Adams, endorsed Cuomo in late October after abandoning his own independent bid.

ERIC ADAMS (D), Mayor of New York: And I'm going to fight for the family with Andrew Cuomo.

WILLIAM BRANGHAM: In the campaign's closing weeks, Cuomo, running a distant second, has been courting conservative-leaning voters, including trying to turn Mamdani's support for Palestinians against him.

FMR.

GOV.

ANDREW CUOMO: The offense he has shown to the Jewish community, he should be ashamed of himself.

(CHEERING) WILLIAM BRANGHAM: At a gathering in Queens organized with local Jewish groups, some Cuomo supporters described him as a lesser of two evils.

TIM ROSEN, Cuomo Supporter: To be quite frank with you, I'm not a huge Cuomo fan, but I think he's the only one that has even a reasonable shot of defeating Mamdani, and that is my number one priority.

As a Jewish person, with all the antisemitism going on, he wouldn't condemn Hamas in the immediate aftermath of the October 7 atrocities.

He's just a menace and a danger in so many ways.

WILLIAM BRANGHAM: Mamdani has called Israel's actions in Gaza a genocide, and he has been meeting with Jewish leaders across the city.

He's also called out what he says is blatant Islamophobia coming from his opponents, like when Andrew Cuomo recently chuckled after a radio host suggested that Mamdani, who is Muslim, would celebrate another 9/11 terrorist attack occurring.

Mamdani says he is committed to fighting antisemitism and that his views on Israel have no bearing on his ability to lead the city.

ZOHRAN MAMDANI: I look forward to being a mayor for every single person that calls this city home.

And that includes Jewish New Yorkers who may have concerns or opposition to the positions that I have shared about Israel and Palestine.

WILLIAM BRANGHAM: Patrick Gaspard has advised several New York mayors and is an informal adviser to the Mamdani campaign.

He says Mamdani's position on Gaza is not the political drag some analysts believe, noting that polls show more than 70 percent of Democrats oppose providing additional economic and military support to Israel.

PATRICK GASPARD, Democratic Strategist: Where you stand on this issue, on the issue of Gaza and the rights of the Palestinians is almost like the point of entry into the conversation.

I will let you come onto my porch to talk about the things that matter, like public education, policing, quality of life.

But I need to know where you stand on an issue that is troubling my soul every time I go on social media.

ZOHRAN MAMDANI: We have a plan to take the most expensive city in the United States of America and make it affordable.

WILLIAM BRANGHAM: Gaspard also credits Mamdani's canny deployment of snappy social media videos... ZOHRAN MAMDANI: So get ready to see a lot more scary videos of this face on your TV.

WILLIAM BRANGHAM: ... alongside old-school organizing.

His campaign recruited a volunteer army 80,000-strong.

But Gaspard also points to another energizing force.

PATRICK GASPARD: I don't believe that this candidacy is possible at this decibel level if not for Donald Trump's victory.

WILLIAM BRANGHAM: President Trump's fingerprints have been on this race for months, from dropping federal corruption charges against Mayor Adams to publicly suggesting Curtis Sliwa should drop out.

CURTIS SLIWA (R), New York City Mayoral Candidate: I'm not dropping out.

I'm not dropping out.

WILLIAM BRANGHAM: And, most recently, with his deployment of federal agents to round up immigrant street vendors and seize people coming into a federal building for immigration appointments.

Trump has also threatened to arrest Mamdani if, as mayor, he tries to stop these deportation efforts.

DONALD TRUMP: President of the United States: You have a communist running New York, all you're doing is wasting the money you're sending there.

So I don't know that he's one.

And I'm not a fan of Cuomo one way or the other.

But if it's going to be between a bad Democrat and a communist, I'm going to pick that bad Democrat all the time, to be honest with you.

BRADLEY TUSK, Tusk Holdings: If Zohran hires people who are truly talented, independent and good at running their agencies and let them do their jobs, they can do really well.

If everyone has to be a 26-year-old that went to Oberlin and pass a progressive purity test, then we're screwed.

We will see.

WILLIAM BRANGHAM: Bradley Tusk is a venture capitalist and political strategist who ran Mayor Michael Bloomberg's reelection campaign as an independent in 2009.

He says, if Mamdani is elected, he faces big fiscal challenges and will have limited to no power to unilaterally enact some of his promises, including raising taxes.

BRADLEY TUSK: They will use Zohran as the poster child.

WILLIAM BRANGHAM: They being the Republicans.

BRADLEY TUSK: Republicans - - all over the country to indict whoever the Democrat is running for office.

And to a certain extent, if he proves to be a decent mayor, that will have less teeth to it.

SEN.

CHUCK SCHUMER (D-NY): Hello, everybody.

WILLIAM BRANGHAM: That's one reason, Tusk says, national Democrats, like Senate Minority Leader Chuck Schumer, are so weary about Mamdani.

The Brooklynite senator has not endorsed him.

Do you think that there is something that the Democratic Party could learn from Mamdani's success?

BRADLEY TUSK: Sure, a lot.

A lot.

I mean, one, he has a positive, affirmative message.

If you look at the Democrats, especially in Washington, I couldn't tell you what their message is, other than that they're unhappy.

WILLIAM BRANGHAM: Back in Queens, Mamdani was joined by two other Democratic socialist stars, New York Representative Alexandria Ocasio-Cortez and Vermont Senator Bernie Sanders.

Their plea in the final days of the campaign, don't take any momentum for granted.

ZOHRAN MAMDANI: They will attack us from every conceivable angle, but we will not bend.

(CHEERING) ZOHRAN MAMDANI: New York is not for sale.

(CHEERING) WILLIAM BRANGHAM: For the "PBS News Hour," I'm William Brangham in New York City.