(John Minchillo/AP Photo)

Former Rep. Anthony Weiner has said he won't get out of the New York City mayor race, but a new poll shows that he has gone from being a front runner to fourth place in just two weeks.

According to a new Quinnipiac poll, which showed Wiener near the head of the pack just two weeks ago, he now trails City Council Speaker Christine Quinn, Public Advocate Bill de Blasio and former Comptroller William Thompson.

In the poll of likely Democratic primary voters, only 16 percent said they would vote for Weiner. Asked whether he should drop out of the race, 53 percent said that he should.

A majority, 65 percent of voters, said that Weiner's behavior - which included recent revelations that he sent lewd messages to women online even after he resigned from Congress - is a legitimate issue in the campaign. And a new high of 40 percent of voters said it should disqualify him, compared to 23 percent when the question was asked last week.

"As I've said before, polls don't change anything," Weiner said in a statement responding to the poll. "But I continue to be grateful and humbled by the continued support of so many New Yorkers who are willing to give me a second chance."

On the campaign trail today, Weiner bristled at questions about why he remains in the race despite calls for him to withdraw.

At an event in Flushing, Queens, Weiner dismissed the Sunday show "talking heads" and "politicians" calling for him to resign. He did not specifically name David Axelrod, a former adviser to President Obama, who said on Sunday that Weiner should "go away," or mention a report in the New York Post that Bill and Hillary Clinton are displeased with his candidacy.

"I don't take my cues on policy from the Sunday talk shows and the pundits. I never have. I don't take my cues from the headline writers in the newspapers. I never have," he told reporters today.

The new poll numbers may not sway Weiner, who defiantly sent a message to supporters today denouncing "TV pundits," "newspaper publishers" and his opponents for trying to stop his campaign.

"So here is what I learned this weekend - a lot of people who don't have a vote want to decide who our next mayor will be," Weiner said in an email.

"I knew that revelations about my past private life might come back to embarrass me. I never hid from that possibility," Weiner added. "But, I waged this campaign on a bet that the citizens of my city would be more interested in a vision for improving their lives rather than in old stories about mine."

He promised to publish another book of ideas for New York and that he wouldn't yield to the calls for him to step aside.

Weiner's 31-year-old campaign manager, Danny Kedem resigned on Sunday, dealing another blow to his campaign.

ABC News' Ben Waldron contributed to this report.