By Bary Alyssa Johnson (staff@latinospost.com) | First Posted: Jul 24, 2013 07:54 PM EDT

After a new sexting scandal was revealed this week, Democratic hopeful Anthony Weiner spent most of Wednesday warding off criticisms from colleagues, rivals and the media who called on him to drop out of the New York City mayoral race.

Ignoring taunts and jeers, Weiner made it clear that he has no intention of dropping out; nor should he, according to a new poll released on Wednesday that puts him in first place in the first round of the Democratic primary.

Should he bow to pressure and drop out of the race, however, the independent Quinnipiac University survey shows that City Council speaker Christine Quinn would take the top spot with 30 percent of the vote, compared to former Comptroller William Thompson's 26 percent. Public Advocate Bill de Blasio would come in at 20 percent and Comptroller John Liu would hang on to just 10 percent.

As scandal continues to plague Weiner's personal life, those surveyed in the Quinnipiac poll score Weiner at just 17 percent for moral character, compared to Quinn's 57 percent and Thompson's 63 percent.

And while a good number of respondents - 57 percent - say personal moral character is very important in a potential candidate, 86 percent say that a candidate's understanding of their problems is extremely important to them.

"I have posited this whole campaign on a bet, and that is that, at the end of the day citizens are more interested in the challenges they face in their lives than in anything I have done embarrassing in my past," Weiner told reporters on Wednesday morning. He added that "this is not about me," but about the voters.

If Weiner stays in the race, he's projected to reign in 26 percent of the vote in the primary election, compared to Quinn's 22 percent and Thompson's 20 percent.

However, director of the Quinnipiac University Polling Institute Maurice Carroll urges voters to focus on what he deems the most important race, the Democratic primary runoff.

"After the new flood of stories about Congressman Anthony Weiner, we must look at the likelihood of a runoff between Council Speaker Christine Quinn and former Comptroller William Thompson," Carroll said. "As of today, those numbers show Thompson ahead in that race."

Indeed, in a runoff the poll shows that Thompson would lead Quinn 51 to 42 percent and would top Weiner 52 to 41 percent. In the unlikely event of a Weiner-Quinn runoff, the poll shows a tie with 46 percent for Quinn and 44 percent for Weiner.

For this survey, Quinnipiac polled 1,340 New York City registered voters between July 18 and 23. Included in the respondents were 507 likely Democratic primary voters and 96 likely Republican primary voters.

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