Last week the mayor was calling the United Federation of Teachers the “number one” impediment to progress in his Children First education reform.

But before the ink was dry on press accounts of the mayor’s tirade, his aides, including Deputy Mayor Kevin Sheekey, were in negotiation with the union to get it to end its campaign against the new round of reforms. As a result, the mayor is willing to drop his plan for Weighted School Funding in exchange for de facto acquiescence to the new restructuring by the UFT and its coalition of parents and officials, the Working Families Party, and the community organization ACORN.

The two sides have settled on these terms, called a “détente.” This has driven a wedge between members of the coalition committed to fighting the new restructuring plan. Parent groups and many public officials, including the comptroller, William Thompson, and the public advocate, Betsy Gotbaum, are uncomfortable with any deal with the mayor. The leading parent group, the Chancellor’s Parent Advisory Committee, has refused to sign on.

Randi Weingarten’s bid for peace is backed by the Working Families Party and ACORN. This is not surprising since the WFP is directed by Gotham’s labor unions, and ACORN is Ms. Weingarten’s partner in the UFT’s high-stakes effort to organize the state’s home health care workers.

A protest rally in front of City Hall, scheduled for May 9, has been put “on hold,” which is, I’m told, a euphemism for “cancelled.”

Under the mayor’s school funding proposal, funds allocated to the schools would follow the student — an exact dollar amount that for the most part wouldn’t vary from school to school. Principals will have to find a way to provide all mandated services within that allocation. The plan gets sticky when the salaries of teachers vary from school to school within the system.

Currently, staff is assigned to schools based on the number of students and budgeted based on a system-wide average salary. If a school is successful at retaining its senior teachers, who pull down high salaries, or can lure them from other schools, they are held fiscally harmless under the status quo.

Senior teachers feel that the new funding formula would trap them in their current schools because principals in other schools may consider them too expensive. This is why the union wanted to quash this program. To save face, the mayor is hiding his capitulation by saying the funding issue will be studied by a “task force” comprised of the UFT, the New York Immigration Coalition, and the Annenberg Foundation.

The mayor is intent on neutralizing his opposition and may now have succeeded. Political aides to the mayor fear that the education issue could undermine his nascent presidential bid.

The turmoil over the mayor’s education initiatives also has led to serious questions being raised by key leaders in the city’s business and philanthropic communities, up to now the mayor’s strongest supporters. They were summoned to Gracie Mansion on Wednesday in an effort by the mayor to retain and indeed increase their support. The mayor asked them to provide funding for a “public relations offensive” to help sell the increasingly skeptical public on the reforms, and many agreed.

It is the assumption of those close to the mayor, I’m told, that without the funds and resources of the teachers union, and the organizational skills of ACORN and the Working Families Party, the parent rebellion would be crushed. However, within the administration, Chancellor Klein is said to have opposed any concessions to the UFT, which mirrors the conventional wisdom regarding the last two teacher contract negotiations, which the chancellor was rumored to have opposed internally.

Among the union, parents, and elected officials, there is similar conflict. In trying to sell the agreement to the uncomfortable parent groups, speaking on a conference call, Ms. Weingarten termed officials of the Department of Education as “absolute and complete assholes” who “can’t be trusted.” To the dissident parents, upset with the lack of even a firm written agreement, she held out the possibility of “rescheduling the May 9th rally” should Tweed renege on the deal.

Before the “détente” was arrived at, many parent leaders believed “we’ve got them where we want them,” wanting no concessions, and preferred holding out for the state Legislature to modify — or eliminate — mayoral control.

To them the mission was not to protect the interests of senior teachers looking to retain their ability to move about the system, but to “put the public back in the public schools.”

For the short run they will have to be satisfied with the better deal for the union.