For months, United Federation of Teachers President Michael Mulgrew withheld his union’s support for Bill de Blasio’s tax hike proposal to fund pre-kindergarten.

Back in August, when Mulgrew was campaigning for de Blasio’s rival Bill Thompson, he argued that the real problem with expanded pre-kindergarten wasn’t the amount of funding, but the way it was targeted. Last month, he said he needed to see the finer details of de Blasio’s plan before throwing his lobbying muscle behind the tax-hike, which is not supported by Gov. Andrew Cuomo.

Those details still aren’t fleshed out, but Mulgrew said today that he’s seen enough to have been convinced. Standing with a host of other labor leaders at a press conference in a vacant pre-K classroom in East Harlem, Mulgrew pledged to lobby state lawmakers who are showing the same kind of tepid support for de Blasio’s proposal that he once did.

“The nuts  and bolts of this is really what our concern was,” said Mulgrew, who added that a meeting with de Blasio’s staff changed his mind. “You could really tell … that they really have engaged themselves in a meaningful way to try to not just figure out the funding source, but figure out how to make this work for the entire city.”

The union-backed support for de Blasio’s plan could be a big boost for the mayor, who campaigned on a promise to expand full-day pre-kindergarten access to as many as 50,000 children. He spent much of his transition period as the mayor-elect touting the plan and lining up allies to publicly support it.

The tax plan, which would also fund a longer school day for middle school students, taxes New York City residents earning more than $500,000 and would yield an estimated $530 million annually.

The tax hasn’t been embraced by Cuomo, a Democrat, or state Senate Republicans, and they could be hard to sway in an election year where they are stressing efforts to lower the cost-of-living for New Yorkers. Cuomo hammered home that point this morning in a press conference that overlapped with de Blasio’s.

At the press conference, Cuomo said he supported the idea of expanded pre-K, but once again declined to endorse de Blasio’s vision for funding it. Cuomo is scheduled to lay out his legislative agenda for the year on Wednesday when he delivers his fourth state of the state address.

Mulgrew joins a growing list of Democrats to convert from skeptics to supporters of de Blasio’s plan now that the candidate has become mayor. Last month, both state Senator Diane Savino and American Federation of Teachers President Randi Weingarten reversed their critiques of de Blasio’s proposal. Like Mulgrew, both had endorsed Bill Thompson during the primary.

In August, just weeks before the primary election, Mulgrew praised Republican state Senator John Flanagan and the rest of the state legislature for providing adequate pre-K funding. But he said that some couldn’t be used because it was designated for half-day seats, an inconvenience for working parents.

“How many millions of dollars are sent back to the state that are allotted for pre-K every year?” Mulgrew said at an August panel, directly addressing Flanagan. “So when everyone talks about expanding it, we’re not even utilizing the very tax dollars that you guys are sending to the districts.”

De Blasio went on to win both the Democratic primary and general election by wide margins, and polls have shown widespread support for his tax plan.

Following Thompson’s loss in the primary, Mulgrew quickly switched the UFT’s endorsement to de Blasio. Mulgrew said that his skepticism about de Blasio’s pre-K proposal was based on decades of promises from politicians to expand pre-K with little to show for it.

“We’ve heard about it for generations and we think we are at a moment in time where we can actually get it done,” Mulgrew said today.

De Blasio said that he had no intentions to back off his proposal once budget negotiations get underway in the coming weeks.

“We will pass this tax in Albany to guarantee full-day pre-K for every child in the city, to guarantee after school for every middle school child,” de Blasio said. “I will repeat it and repeat it and repeat it again until it’s done.”