Rep. Anthony Weiner walked through the door at 50/52 Broadway last Thursday afternoon, rode the elevator up to the 14th floor, and took a seat in the office of the president of the United Federation of Teachers.

Mr. Weiner became the latest would-be mayor to meet with the Randi Weingarten, who leads the city’s 80,000 teachers and 60,000 other school workers. All of the Democratic contenders have met with Ms. Weingarten, except for C. Virginia Fields, whose scheduled meeting was postponed because of last month’s blizzard.

Pilgrimages to the offices of the teachers union were not rare in past years – even Mayor Bloomberg went in for a school chat before his election – but this year, as teacher contract negotiations remain stalled and Democratic candidates prepare to poke holes in Mr. Bloomberg’s education record, political experts said Ms. Weingarten has become something of a kingmaker.

“Everybody who’s seeing her now regrets they didn’t six months ago,” a political consultant, Norman Adler, said. “Everybody wants to be the first one in the door.”

Whichever candidate wins the endorsement of the United Federation of Teachers will also secure votes, campaign volunteers, and information.

“The teachers know where all of the problems are that the mayor may not be owning up to,” Mr. Adler, who for 11 years was director of political action and legislation for District Council 37, the city’s largest union, said. “Whoever gets the endorsement probably gets some very good information.”

Another political consultant, Hank Sheinkopf, said: “Because education is the no. 1 issue in the minds of New York … the teachers union endorsement can be very, very helpful.” That, he said, is especially true in such a crowded field.

In the 2001 race, the UFT’s endorsement did not live up to its reputation. The union endorsed the comptroller, Alan Hevesi, in mid-August, before the Democratic primary. He lost. In the runoff between Fernando Ferrer and Mark Green, the union endorsed Mr. Ferrer. He lost. In the general election, the union endorsed Mr. Green, who lost to Mr. Bloomberg.

Mr. Sheinkopf said the less-than-spectacular record of four years ago doesn’t matter.

“That is past tense,” he said. “All politics is in the present tense, and education is going to be the no. 1 issue.”

A professor of political science at Baruch College, David Birdsell, said any New York candidate would be “foolish” to discount the teachers union this year, because of its people power and because of education’s centrality in this fall’s campaign. Also, he said, the union’s power to boost a candidate could help push the Bloomberg administration toward a compromise on the teachers contract.

“There are precious few points of leverage during the year. One point of leverage is when the mayor faces political opposition,” Mr. Birdsell said. “There’s every reason to try to seek maximum political advantage.”

While the mayor would probably appreciate union support, Mr. Birdsell said, he probably doesn’t need it. Mr. Bloomberg could follow the lead of successful Republican candidates elsewhere, who have explained away labor opposition by saying the unions are defending the status quo while their administration would implement fundamental reform.

In a telephone interview yesterday, Ms. Weingarten said she suspects the Bloomberg administration is avoiding a contract resolution to help the mayor win re-election.

“They over promised the public and they haven’t delivered on their promise,” she said. “They now need someone to blame.”

Ms. Weingarten said it’s too soon to say when or if the UFT’s delegate assembly will choose to endorse somebody for the primary or the general election. But she said the Democratic candidates are asking good questions, presenting interesting ideas, and telling her their constituents complain about some of the same problems in the Bloomberg-controlled schools that the union has highlighted.

Ms. Weingarten said she doesn’t yet know how the Democrats will differentiate themselves from the mayor and from each other on education, but one thing is for sure: Education will be “very politicized in this election.”

She said teachers thought that when Mr. Bloomberg won control over the school system in 2002 he would create a “demilitarized zone” where real improvements could be made. “But that’s not what it turned out to be,” she said, “so as a result the mayor will be subject to a lot of criticism.”

Indeed, the candidates have been quick to criticize the mayor’s education policy – and they’re eagerly seeking the teachers’ support. Mr. Weiner, who delivered a speech last week about his education ideas, said his sit-down with the union boss went “swimmingly.”

“The UFT is important and Randi Weingarten is important,” the congressman said in a telephone interview. “It’s always been, and will continue to be, an influential union.”

Mr. Weiner said he and Ms. Weingarten share concerns about what they view as a breakdown in discipline, the increasing difficulty of attracting and retaining top-notch teachers, and the paucity of school funds making their way into classrooms.

“This is emerging as a noisier and noisier drumbeat of concern in the electorate. I think the mayor hears it and I know I hear it,” Mr. Weiner said. “These are all problems that are the direct result of mistakes made under the mayor’s control.”

A spokeswoman for Fernando Ferrer, Jennifer Bluestein, said Mr. Ferrer will continue to meet with key leaders such as Ms. Weingarten throughout the city.

“Our school system continues to face challenges, from overcrowded classrooms to a shortage of after-school programs, and Fernando Ferrer has consistently provided innovative and bold solutions so that all our kids have the opportunity to get a great education, as he will share with New Yorkers in coming months,” she said.

The speaker of the City Council, Gifford Miller, another likely mayoral contender, meets with Ms. Weingarten regularly about education issues – usually in his capacity as council speaker but also as a candidate – his campaign manager, Brian Hardwick, said.

“Education is a key priority for Gifford, both in his work on the City Council but also on his vision of how we create a better future,” Mr. Hardwick said. “This is going to be a central issue to his campaign. He believes that when the mayor said, ‘Judge me on education,’ that the mayor meant it.”

Ms. Weingarten said the only candidate who hasn’t reached out to her is Mr. Bloomberg. But she said she wouldn’t rule him out yet for a UFT endorsement.