The collaboration between cities and advocacy groups, however, has not always gone smoothly, according to a review of hundreds of pages of public records, obtained through Freedom of Information requests in nine major cities, including Chicago, Los Angeles, Philadelphia and San Francisco.

In January, New York officials clashed sharply with an outside counsel over the group’s first major project: an amicus brief that Cities United filed in support of Mr. Obama, in federal court in Texas. At the recommendation of the National Immigration Law Center, the coalition retained a Los Angeles firm, Andrade Gonzalez, to prepare the document.

Sean Andrade, a founder of the firm, said he suggested that Cities United list mayors from Texas as the major litigants in the case. Officials in New York disagreed, preferring to name New York City and Los Angeles as the chief litigants.

To Mr. Andrade’s dismay, New York officials also demanded that his firm’s name be removed from the brief.

[. . .]

The spat, however, raised lingering doubts: In an email shortly afterward, Mr. Noorani, president of the National Immigration Forum, asked a top Los Angeles city official for her assessment of a Cities United proposal, “given the incredible amount of drama they kicked up on the amicus.”

But conditions in Times Square have recently come under scrutiny, with some New Yorkers complaining about the proliferation of street performers — including, most notably, topless women wearing body paint — who are said to be accosting pedestrians for tips for posing for photographs.

Mr. de Blasio has been keen to demonstrate that he is addressing the concerns, and on Thursday he announced a task force to consider ideas on how to better prevent activities that the city deems illegal or harmful to the area’s quality of life.

But the mayor, at a news conference in Queens, surprised many urban planners when he said he would give “a fresh look” to whether the pedestrian plazas should remain.

Nearly 600 days into his tenure, the horses are still clopping. And the mayor has a new message for activists: Talk to somebody else.

“What I would say to every advocate is, you already have my vote; go get the votes in the City Council,” Mr. de Blasio said in a radio interview on Wednesday, when the host, WNYC’s Brian Lehrer, asked about the holdup. “Solidify the support in the City Council so we can make this change.”

[. . .]

“We have a government that is very effective, and people all over the city know we are trying to do things for everyday New Yorkers. It is self-evident.”

[. . .]

“I’m an object lesson in why people shouldn’t listen to mainstream polling that much. I wouldn’t be sitting here in this role.”

[. . .]

“[My team] can always communicate things better.”

[. . .]

“I think there’s a huge dichotomy between what’s happening in the mainstream media and what people are feeling and understanding.”

[. . .]

“[Michael R. Bloomberg] was covered in a very particular fashion. I think the media had a kind of kid-glove sensibility toward him. I think that’s well-established.”

[. . .]

“A miscommunication. She went ahead of the team. We corrected it right away. If you want to write about it, God bless you, but I wouldn’t overrate it.”

[. . .]

“There’s no question in my mind we’re doing the most important work, we’re staying with our vision. I have no doubt that when you add it up, millions of people are being touched by it.”

[. . .]

Rauh later tweeted that it appeared that de Blasio had slipped out a side entrance even though he usually exits the gym through the front door.

“Mayor always exits gym through front door. Apparently even he realized how bad that visual would have been today,” Rauh tweeted.

De Blasio Press Secretary Karen Hinton said that the mayor was on his way to the hospital when asked at 11:25 a.m by DNAinfo regarding his whereabouts.

Asked why the mayor did not leave the gym even though the standoff was ongoing, Hinton said “he was on the phone” with Police Commissioner Bill Bratton and Fire Commissioner Daniel Nigro regarding the incident.

Hinton later tweeted that the mayor “spoke with Fire & Police Commissioners several times by phone on shooting early morning & at gym. At gym for 80 min.”

An employee at Colson Patisserie which is located near the Y on 9th Street and Sixth Avenue, said that the mayor had been there.

“Why could anyone think it’s OK for him to be at a gym working out for two hours in the middle of the day and he is supposed to be running the city,” said a former top official who worked closely with two mayors.

Another former official who was involved in the city’s response to several major crises, called the mayor’s decision “unbelievable.”