The NBC 4 New York/Wall Street Journal/Marist Poll of 1,199 New York City adults was conducted Wednesday, after Weiner publicly acknowledged he texted sexual images to women after resigning his House seat for similar behavior in 2011.
The poll found City Council Speaker Christine Quinn is favored by 25 percent of Democrats, with Weiner slipping to second place at 16 percent, ahead of Public Advocate Bill de Blasio and former Comptroller Bill Thompson, tied at 14 percent. In the most recent previous NBC 4 New York/Wall Street Journal/Marist Poll, conducted in June, Weiner led the field with 25 percent, followed by Quinn at 20 percent, Thompson with 13 percent and de Blasio with 10 percent.
The poll released Thursday found 43 percent of New York Democrats want Weiner to get out of the race.
Also Thursday, U.S. House Minority Leader Nancy Pelosi, D-Calif., said the behavior of Weiner and San Diego Mayor Bob Filner -- also a Democrat, who has been accused by at least three women of sexually inappropriate behavior -- is "reprehensible," The Hill reported.
"The conduct of some of these people that we're talking about here is reprehensible," Pelosi told reporters on Capitol Hill.
"It is so disrespectful of women, and what's really stunning about it is they don't even realize," she said. "They don't have a clue."
"If they're clueless, get a clue," Pelosi said. "If they need therapy, do it in private."
Weiner and Filner both served in the House when Pelosi was speaker.