Embattled New York mayoral candidate Anthony Weiner is pressing on with his bid to lead America’s largest city – even if he’s dogged by hecklers on the campaign trail, as well as late-night comedians giddy with jokes about Carlos Danger “selfies” and sex-chat paramour Sydney Leathers.

Mr. Weiner stopped Thursday at Masbia Flatbush, a kosher soup kitchen, to peel carrots and help volunteers prepare meals for this “free restaurant” in the heart of an Orthodox Jewish neighborhood in Brooklyn. He was promoting his plan to establish a “nonprofit czar” for the city, a liaison between the mayor’s office and charitable organizations.

Although his wife, Huma Abedin, a close adviser to former Secretary of State Hillary Rodham Clinton, did not attend the event, Weiner has given no indication he plans to drop out of the race. Even as editorials and national leaders have urged him to do so, he has insisted that the race should be about the issues that matter to New Yorkers – not about him.

But with his lead in the race all but evaporated, according to a poll released Thursday, many are asking, do his policy positions even matter anymore? Is he still a viable candidate?

If he’s not, what’s the point of continuing?

“Citizens have a right to decide for themselves whether this personal behavior ... is important to them,” Weiner said to a host of reporters at Masbia. “I understand I brought this upon myself, but I want to return to having a conversation. I don’t know if I’ll have a chance to, but I certainly want to try.”

It’s a conversation proving more and more difficult – attested to by the fact that one woman interrupted the event to shout, “I’m a neighborhood resident and I’m an observant Jew, and we want nothing to do with the likes of Anthony Weiner!” The woman was asked to leave by kitchen workers, yet even so, there was little talk about his idea for a “nonprofit czar.”

Weiner’s lead over his rivals in the polls is now gone. He currently trails City Council Speaker Christine Quinn, who has retaken the front-runner’s mantle with 25 percent of the city’s registered Democrats, according to Thursday’s NBC 4 New York/Wall Street Journal/Marist poll.

Still, Weiner is second with 16 percent, a statistical tie with Public Advocate Bill de Blasio, who has 14 percent, and with last mayoral election’s runner-up William Thompson, also preferred by 14 percent of primary voters.

“I don't think Weiner can win now,” says Larry Sabato, director of the Center for Politics at the University of Virginia in Charlottesville. “I'll even be mildly surprised if he makes the runoff. There's just too much sleaze in the headlines, and even in this age of remarkable public tolerance for sins of the flesh, there are limits. Weiner's reached them.”

Yet the candidate still boasts a campaign war chest of more than $4 million – dwarfing all his rivals except for Speaker Quinn. And he’s eligible for $1.5 million more in public matching funds – money he would lose if he doesn’t spend it on campaigning this year.

“It’s that kind of use-it-or-lose-it situation,” says Kenneth Sherrill, professor emeritus of political science at Hunter College in Manhattan. “He might easily come to the conclusion it might be rational that he should use this money to stay in the race.”

Professor Sherrill, a veteran observer of mayoral elections in New York City, can envision a scenario where a campaign now, even if unsuccessful, could have benefits. “He could use this money he has to run a thoughtful campaign,” he says. “Perhaps he could be in a position four or eight years from now to say, ‘Look, I said very wise things back then: History shows me to have been right,’ and to come back. That may be a very sensible strategy.”

Indeed, those still supporting Weiner do so with far more enthusiasm and commitment than Quinn or Mr. Thompson receive at this point, according to the Marist poll. More than half of Weiner’s supporters say they “strongly” support the candidate, compared with 37 percent of Quinn’s and 35 percent of Thompson’s.

And while over a quarter of Quinn’s supporters say they “might vote differently” in the election, only 15 percent of Weiner’s current supporters say this.

The generally tepid support for the rest of the candidates, in fact, was one reason Weiner shot to the top of the polls since he announced his candidacy in May. Long known for his combative and, to many of his colleagues, irritating style, Weiner retains his appeal with at least a certain base of New Yorkers.

“I think that he may have a base among Giuliani Democrats – who certainly didn’t desert [former mayor Rudolph] Giuliani when he was a flagrant philanderer,” Sherrill says. “There’s a corps of voters who prefer a more aggressive mayor. There’s a real desire for a mayor who understands the everyday life of New Yorkers, and he is pretty good at communicating his street smarts. He does a good job communicating, getting the feeling of everyday life for working-class New Yorkers.”

Yet the Marist poll also shows that negative opinions of Weiner have soared since revelations he continued to send lewd selfies to Ms. Leathers, a young woman in Indiana who is now seeking to peddle her story to tabloid TV shows. Nearly 6 in 10 registered Democrats now have an “unfavorable” view of Weiner, compared with only 1 in 3 last month, before the scandal broke.

His “favorable” ratings, too, have plummeted 22 points among potential primary voters – from 52 percent in June to only 30 percent, according to the poll.

“A Weiner mayoralty is hard to contemplate,” says Dr. Sabato, who also runs Sabato’s Crystal Ball, a website that keeps tabs of polls and predicts election results. “The Big Apple would become a standing national joke as long as he was mayor. Any controversial actions a Mayor Weiner took would generate endless variations of the joke.”

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Even so, Weiner is carrying on, trying to persuade a majority of people disgusted with his online behavior to listen to his ideas for the city.

“This is a very competitive and aggressive man who doesn’t mind making enemies,” Sherrill says. “I really think that unless his wife tells him to throw in the towel, he is not leaving.”