But last year, Mr. de Blasio’s administration, eager to keep a lid on water and sewer rates that had grown by an average of 8 percent annually under Mr. Bloomberg, moved financing for the third tunnel to other projects, Amy Spitalnick, a de Blasio spokeswoman, said.

The city intends to finish the remaining portions of the tunnel sometime in the 2020s, but it has not set a date for completion nor allocated money in the budget to carry out the work. For the foreseeable future, the $6 billion tunnel will remain dry in the two largest boroughs, where well over half the city’s population lives.

“You look back over the last 50 years, whenever there were fiscal pressures, the unseen world of the municipal water system is where weak city leaders turned to cut spending,” said Kevin Bone, a professor of architecture at Cooper Union and an editor of “Water-Works: The Architecture and Engineering of the New York City Water Supply.” “I’m disappointed to hear that they’ve deferred it. It is symptomatic about planning for the future in America.”

[. . .]

Harold M. Ickes, the lobbyist, was a towering figure — a member of a prominent liberal family, a trusted counselor to Bill and Hillary Clinton and a former White House deputy chief of staff. But his firm’s appeals to the administration of Mayor Michael R. Bloomberg were rebuffed.

The man who would one day succeed Mr. Bloomberg, however, was more receptive.

That man, Bill de Blasio, then a councilman from Park Slope, Brooklyn, embraced Mr. Ickes’s cause, sponsoring a resolution calling for a review of the policy and accusing city officials of “radically” changing menus without listening to parents’ concerns.

“The bottom line, in my view, is milk is unlike almost any other food in its fundamental nature,” Mr. de Blasio said at the time. The policy stayed in place, but the dairy industry later thanked Mr. de Blasio for his “leading efforts on this issue.”

On his path to becoming mayor, Mr. de Blasio, a Democrat, has long leaned on Mr. Ickes, whom he calls his closest mentor. A friend for three decades, Mr. Ickes, 76, has advised Mr. de Blasio’s campaigns, introduced him to wealthy donors and recommended him for a breakthrough job managing Mrs. Clinton’s run for United States Senate in 2000.

Mr. de Blasio, a politician who values loyalty deeply, has found ways to give back.

Shortly after the mayor’s election in 2013, Mr. Ickes opened a New York branch of his lobbying firm. Although he had not lobbied in the city for nearly a decade, Mr. Ickes proved a quick study, collecting about $1 million in fees and securing wins for major clients.

Among his victories, one stands out: At Mr. de Blasio’s urging, the City Council passed an unusual bill in 2014 that gave $42 million in wages to public school bus drivers represented by Mr. Ickes. The wages came on top of an existing city contract, raising objections from some council leaders and government watchdog groups.

In emails to aides to Mr. de Blasio, Mr. Ickes personally suggested changes to the bill’s language, records show.

It was a proposal in which the mayor invested a extraordinary amount of political capital. The result has alienated, in no particular order, park advocates, council members, union leaders, community boards, real estate interests, pedicab drivers, political donors, and, ultimately, animal-rights activists.

[. . .]

The thing that makes this particular debacle so unusual isn’t that the stakes were high, but that they were so very low. All mayors lose big battles, but here was the spectacle of a mayor taking a high-profile stand on a matter of importance primarily to one of his donors, and then refusing, in defiance of his critics, allies and all political common sense, to let it go.

“They’re not humane,” he said in 2013, before he took office. “They’re not appropriate to the year 2014. It’s over. So just watch us do it now.”

And so he tried, with the staunch backing of New Yorkers for Clean, Livable and Safe Streets — an organization bankrolled by a wealthy real estate executive that helped knock his rival Christine Quinn out of the mayoral race.

“It always just bothered me seeing those horses,” said the executive, Steve Nislick, in an interview in 2014 about his motivations and what he wanted from the man he helped elect. “I just knew from my own experience that horses don’t belong in the middle of New York City traffic.”

Ultimately, Nislick and de Blasio settled for a compromise. The horse carriage industry would be drastically reduced and housed inside Central Park. The city would pay some $25 million to repurpose an old building for the cause. Pedicab operators would be banished from the tourist-heavy southern portion of the park. The city announced that a deal had been reached.

Then it began to fall apart. The Central Park Conservancy and surrounding community boards panned it. The editorial boards reacted with horror. The Transport Workers Union organized the pedicab drivers and promised a lawsuit. The Teamsters, who represent the drivers, agreed to support the deal, until they didn’t.

But the amount of the raise is notably higher than what the commission suggested — an increase of about 23 percent, to $138,315, from their current base pay of $112,500 — and some feared that the higher salaries might be a result of a different sort of concession, tied to the mayor’s plan to shrink the horse-carriage industry in Manhattan.

The machinations to sign off on the pay bill were occurring under a deadline of sorts: Because the bills were finalized by the end of the day on Thursday, they could be voted on next Friday, the same day the Council is expected to vote on the horse-carriage plan.

Several Council officials described a full-court press by City Hall, including from Mr. de Blasio’s top political adviser, Emma Wolfe, to secure Council support for the horse-carriage bill, an initiative that has been a top goal of wealthy political supporters of the mayor, a Democrat.

The City Hall officials were said to be focusing on city lawmakers alarmed by a hearing last week, where administration officials could not answer basic questions about some of the bill’s provisions, like the cost of a new stable in Central Park.

The apparent timing of the votes came despite the objections of some Council members, who believed it created an unseemly appearance, and could undermine what they believe is the sound policy of the pay bill, according to several people familiar with the conversations.

Last week, the company’s Queens application was rejected, along with those of two rival promoters, after local opposition. Instead, A.E.G. Live was given clearance to hold a festival in July on Randalls Island; its rivals, Madison Square Garden and Founders Entertainment, did not receive similar permission to hold their events.

On Jan. 11, the day the Randalls concert was announced, Mr. Ickes and his lobbying partner, Janice Enright, contributed $400 to Mr. de Blasio’s campaign account, the limit for a registered lobbyist. Mr. Ickes’s wife, and the wife of his other partner, Kevin McCabe, each gave $4,950, the maximum allowed by law, financial records show.