(CNN) - Candidates vying to become the next mayor of New York displayed deep disagreements in a televised debate Wednesday over the city's controversial stop-and-frisk searches, which a federal judge said earlier this month violate the Constitution by targeting minorities.
While all of the Democratic candidates have proposed reforms to the policy, frontrunners Christine Quinn, the City Council speaker: and Public Advocate Bill de Blasio sparred over the substance of how the controversial policy would change under their watch.
De Blasio, who said he'd replace Police Commissioner Raymond Kelly and appoint an independent inspector general, said he was the only candidate on the stage who would take sufficient steps to end stop-and-frisk searches.
But that statement, which echoes a television ad de Blasio has run in New York, drew outrage from his rivals, who said he was misleading voters by claiming other candidates would not also change the current law.
"Stop lying to the people of New York City," demanded former comptroller Bill Thompson, who said he "didn't need lectures" from de Blasio on the issue.
Quinn - who polls show is running neck-and-neck with de Blasio, and leading Thompson - asserted that her planned vote Thursday to override a veto by Mayor Michael Bloomberg on a police measure amounted to a vote for greater oversight on law enforcement matters.
"Unlike the public advocate - who is really good at telling other people what to do, but not always so good at getting things done - tomorrow we will put legislation into effect that will have permanent monitoring of our police department," she said.
Later in the debate, the jabs between de Blasio and Quinn turned personal when the two candidates addressed comments de Blasio's wife made to New York Times columnist Maureen Dowd, which Quinn called "hurtful and upsetting."
The comments were the subject of scrutiny Wednesday after Dowd was forced to correct her column after initially misquoting Chirlane McCray, the candidate's wife, who spoke about Quinn's stance on family issues.
In the full, correct statement, McCray said Quinn was "not speaking to the issues I care about and I think a lot of women feel the same way. I don't see her speaking to the concerns of women who have to take care of children at a young age or send them to school and after school, paid sick days, workplace, she is not speaking to any of those issues."
Speaking during the debate, Quinn said she took the remark as criticism of her and her wife's decision to not have children. If elected, Quinn would be the first female and first openly gay mayor of New York.
"The decision whether or not to have children is a deeply personal one," she said. "Raising someone's family - we are blessed here in New York to have families of all shapes and sizes - should have never have happened, and it was very hurtful in my household this morning."
De Blasio said that his wife "meant no offense" when she made the remarks, explaining she was simply disagreeing with some of Quinn's stances on paid sick leave and after-school programs.
"I think it was a respectful and substantive statement on the issues that have been the core of this campaign," he said.
Anthony Weiner, a one-time frontrunner in the mayoral contest whose bid was kneecapped after a lewd-messaging scandal, was given less time to speak than the candidates currently leading the field, though he did manage to insert jabs at both Quinn and de Blasio, as well as current New York City Mayor Bloomberg.
Asked a question about disaster preparedness in the city that recalled Bloomberg's vacation to Bermuda during a blizzard in 2011, Weiner blasted the mayor for another weather-related decision in the aftermath of last year's Superstorm Sandy.
"The people in Rockaway were literally digging themselves out of their own homes, and you were reading stories about how the marathon would continue - and some people on this stage supported that idea - it had a discordant sense that struck people to their very core," he said. Eventually the New York City Marathon was canceled last autumn.
Unlike past debates, Weiner's sexting scandal didn't arise Wednesday - expect for a brief moment during the "lighting round," when candidates were thrown yes or no questions by the moderator.
The question was: "Do you ever text and drive?" When Weiner answered "yes," the crowd laughed knowingly.
The most recent public poll in the New York race, a NBC4/Wall Street Journal/Marist survey taken August 12-14, showed de Blasio and Quinn tied at 24% among likely primary voters. Bill Thomson was at 18% and Weiner stood in fourth at 11%.
If a candidate fails to cross the 40% threshold on the September 10 primary, the race turns into a runoff between the top two contenders set for October 1.