He has hammered her over the surging level of fines against small businesses, chided her for not demanding greater oversight of New York’s police and denounced her for failing to support a bill providing paid time off for sick workers.

At times, the mayoral campaign of Bill de Blasio, the public advocate, has seemed like a crusade to shame Christine C. Quinn, a rival in the Democratic primary for mayor, into adopting the most cherished positions of their party’s liberal wing.

His problem: She is starting to do it.

The limitations of Mr. de Blasio’s strategy were laid bare on Friday when Ms. Quinn, the City Council speaker, struck a compromise with liberal advocates and unions to pass the paid sick-leave legislation she had long blocked. Advocates called the agreement imperfect, but still showed up to applaud her at a celebratory news conference.

It was the latest episode in which Ms. Quinn’s deal-making acumen deprived Mr. de Blasio of a potent line of attack, showcasing the power that her incumbency as speaker gives her to outmaneuver opponents in the race for mayor.

Over the past several weeks, amid criticism from Mr. de Blasio, Ms. Quinn has introduced legislation to create a police inspector general and to reduce fines levied on street vendors, seemingly timing her announcements for maximum political effect: her office unveiled the street vendor bill minutes before Mr. de Blasio was to assail her at a news conference at City Hall on the same subject.

As effective as Ms. Quinn’s tactics can be, she runs the risk of appearing more pragmatic than principled, leading some critics to question what, precisely, she stands for.

She had long resisted paid sick-leave legislation, saying that in a tough economy, the requirement would be too burdensome for businesses. But late Thursday, without much warning, she accepted a deal that would require thousands of businesses to provide the benefit, covering more than 800,000 of the 1.3 million New Yorkers who do not currently have it.

As he castigated Ms. Quinn on Friday for not pursuing a more comprehensive bill that would cover more workers, Mr. de Blasio suggested her recent embrace of liberal issues had been belated and cynical.

“That’s not leadership,” the public advocate said at a news conference. “That’s acquiescence to public pressure.”

In a later interview, Mr. de Blasio predicted that Democratic primary voters would see through Ms. Quinn’s reactive approach and favor a candidate more in tune with its liberal wing.

“I’m talking about the values of Democratic voters in New York City,” Mr. de Blasio said. “If the speaker constantly has to reach for that, as opposed to being naturally in that position, it’s a problem for her.”

At City Hall on Friday, Ms. Quinn played down any lingering doubts about the sick-leave compromise, saying she had secured a deal where “all sides ended up having a voice.” Echoing a theme of her campaign, she described it as an example of “what effective policy making is all about.”

The Quinn campaign moved quickly to portray her as an inclusive champion of the middle class, sending a message to supporters in which Ms. Quinn pledged, “I will never stop bringing New Yorkers together.”

But people with knowledge of the negotiations over the sick-leave bill said Ms. Quinn only reluctantly joined the discussions, hours after discovering that a dozen council members had signed an unusual petition that would seek to force a vote on the measure despite her opposition.

Ms. Quinn, seeking to prevent the imminent filing of the petition, said she would discuss a deal. But she at first insisted on a broad exemption for small businesses that employ thousands of workers. Frustrated by the speaker’s position, advocates issued an ultimatum: Unless Ms. Quinn agreed to apply the requirement to businesses with as few as 20 workers, the talks would be off.

On Friday, as they stood with the speaker to celebrate the agreement, advocates still conveyed that Ms. Quinn had played a grudging role in the deal.

“We hit her pretty hard on this, and she got pushed to the point where she needed to negotiate,” said Javier H. Valdes, an executive director of Make the Road, a group involved in the negotiations. “When she did see that writing on the wall, she took a leadership role in finalizing it.”

The feminist writer Gloria Steinem, who had said she would withhold her endorsement of Ms. Quinn if she did not allow a vote on the paid sick-leave measure, thanked the speaker for the compromise. But in a statement, Ms. Steinem pointedly referred to “the 1 percent” that had pressured leaders like Ms. Quinn to block action on the issue.

One of the city’s most powerful unions, 1199, registered a starker form of disapproval, withholding its support for the compromise this week when advocates were asked to endorse it, according to people involved in negotiations.

The murmurs of discontent on Friday provided some solace to Mr. de Blasio, who insisted the paid sick-leave question “remains absolutely alive in the debate about the future of our city.”

Mr. de Blasio said he would join the Rev. Al Sharpton at a weekend rally to call for a more stringent sick-leave measure in New York, and he took pains to explain why advocates were now willing to stand by Ms. Quinn’s side. “As the saying goes,” Mr. de Blasio said, “when a hungry man is offered half a loaf, he will take it.”

Still, hours after Ms. Quinn’s boisterous news conference had ended on the steps of City Hall, it was clear that the day’s political momentum was with her. Shortly after she finished, Mr. de Blasio delivered his remarks, standing behind a spare lectern, all alone.

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