NEW YORK — Mayor-elect Eric Adams’ push to install his preferred pick to lead the legislative body meant to serve as a check on him as City Council speaker has begun to falter, as four people who influence the process continue to oppose his selection, according to seven sources involved in the negotiations.

Adams and his political advisers have been quietly backing Queens City Council Member Francisco Moya in the in-house race to be the speaker, and things seemed to be going their way earlier this week. But over the past few days they have run into opposition from the leaders of two unions — 32BJ SEIU and DC37 — as well as the Democratic Party bosses in the Bronx and Queens — Moya’s own backyard, the people said, speaking anonymously to discuss private deliberations.

Now two of Moya’s chief rivals for Council speaker — Brooklyn’s Justin Brannan and Manhattan’s Keith Powers — are in talks with the labor and party bosses to drop their own bids and get behind Adrienne Adams. She attended the same high school as the new mayor with whom she shares a last name and has fashioned herself as a politically moderate Democrat with close ties to the party boss. In recent days, she has emerged as a strong competitor in the race.

The deal-making has been engulfed in chaos over the past week, as the incoming mayor faces fallout from a foray into local politics after his decisive electoral win this year. He has branded himself nationally as the face of the Democratic Party — a former police captain who supports law enforcement but has personally experienced the abuses of cops. Now his rising star nationally is being threatened at home by this disorganized effort, much of which took place while he was on a spiritual journey in Ghana.

Some incoming Council members — several of whom said in interviews on Saturday that Adams personally reached out Moya’s behalf — have bristled at the notion that a mayor would dictate who should lead the legislative branch of government. Adams himself told the press in September he had no plans of “placing my finger on the scale” in the speaker’s race.

Others are troubled that the mayor-elect and his advisers are pushing a man, given the female-majority makeup of the new City Council. To that end, some penned a letter on Friday calling for a woman to lead the body.

And many have said they prefer other candidates and do not appreciate their wishes being trumped by the incoming administration.

Adams’ spokesperson Evan Thies insisted on Saturday the mayor-elect has not been backing Moya and said he would be content with Adrienne Adams. “Mayor-elect Adams has consistently told leaders that he would be comfortable with a number of speaker candidates,” Thies said by text.

He said Adams would have been happy with several of the options, but was sensitive to the wishes of those hoping for a Latino leader.

Like Moya, Adrienne Adams endorsed Adams in his mayoral primary. Nevertheless, the incoming mayor and his team wanted to support a Latino candidate for speaker, even though some of his top advisers have a close relationship with Brannan, people involved in the talks have said.

Adams continued to call powerbrokers and incoming Council members to advocate for Moya on Saturday, according to three people familiar with the outreach who spoke on condition of anonymity to freely discuss private conversations.

That comes a day after his meeting with Rep. Gregory Meeks (D-N.Y.), who is the Queens Democratic Party leader, in Washington on Friday. During that talk, Meeks and said his borough’s Council delegation was not uniting behind Moya, according to two people familiar with the conversation.

Meeks’ Bronx counterpart, state Sen. Jamaal Bailey, informed Adams that his members felt the same way.

Representatives for Meeks, Bailey declined to comment, as did Brannan and Powers. A representative for Adrienne Adams did not return a message.

Brannan and Powers have been working to win over the incoming Council members and are likely to persuade their loyalists to vote for Adrienne Adams, according to two people familiar with their thinking.

A progressive bloc of legislators has been agitating for either Carlina Rivera or Diana Ayala for Council speaker, arguing the body should be led by a woman of color who will act as a check on the new mayor. Some of those members penned a letter opposing Moya on Friday.

But Rivera and Ayala do not appear to have enough votes at this point to win the race. Neither returned requests for comment.

Moya’s team disputed that he’s in hot water.

“Councilmember Moya has support across the political spectrum and from all of the boroughs. He is working hard to talk with all 51 incoming Councilmembers to understand the needs of the various communities in the city,” adviser David Weiner said.

The latest twist in the behind-the-scenes contest, which will be decided by the 51 Council members next month, has created friction among some of the city’s leading unions. DC37 and 32BJ, which represent municipal workers and private-sector building employees respectively, are angry with the Hotel Trades Council for whipping votes for Moya because the unions had agreed to stick together as a coalition, four sources told POLITICO.

Meanwhile, some Council members have questioned whether a mayor should have a role in picking a legislative leader.

“The noise that I’m hearing is not from the members, and that’s where it becomes very uncomfortable to me because we’re the members. A lot of the rumors that are being started and swirled around are not from members,” incoming Bronx member Althea Stevens, who is supporting Ayala, told POLITICO earlier this week.

Camille Rivera, a Democratic consultant involved in an organized push for a female speaker, concurred.

“The mayor has to deal with an economy post Covid, he has to deal with small businesses closing, he has to deal with homelessness,” Rivera said. “This should not be the fight.”