As the city teachers union head, Randi Weingarten, enters the national scene by marking her first full day as president of the American Federation of Teachers, the city’s schools chancellor is also reaching out beyond New York.

As part of Joel Klein’s new Education Equality Project, the effort he kicked off last month with the Rev. Al Sharpton, the chancellor has been spending the summer break promoting to the presidential candidates his philosophy of how to improve public education.

He and Rev. Sharpton were in Chicago yesterday meeting with campaign staffers for Senator Obama.

Education Equality Project members have also met with Senator McCain’s campaign, and Mr. McCain has told the group he is considering signing onto the project, a source with the group said.

A spokesman for Mr. McCain, Peter Feldman, did not say whether Mr. McCain would sign onto the project, but he did praise it: “Senator McCain applauds the efforts of the Education Equality Project and the commitment of New York’s education officials to this effort. What these outstanding individuals understand and embody is the critical importance of strong leadership in education, not just at the administration level, but at the classroom level.”

If Mr. McCain signs onto the project, he could do so as soon as tomorrow, when he is set to unveil a full education plan in a speech to the National Association for the Advancement of Colored People.

The Education Equality Project is a nonpartisan effort, and it would not endorse a candidate. But Mr. McCain’s support would deliver a big boost to the project, which aims to promote certain kinds of education policies, such as the ability to fire ineffective teachers, accountability plans, and charter schools.

The pairing could be a natural next step for Mr. McCain, who has lately been sounding some notes in synch with Rev. Sharpton and Mr. Klein. In a speech to the National Council of La Raza’s convention in California yesterday, Mr. McCain said he supports charter schools, efforts to “weed out” incompetent teachers, and plans to “hold schools accountable” for their results. He also called improving schools attended by poor students “the civil rights challenge of our time” — the same phrasing Mr. Klein often uses.

The New York Post yesterday reported that Mr. McCain built his education plan after consulting with Mr. Klein.

A signatory of the project, Jeb Bush, a former Florida governor, would not say whether Mr. McCain is signing onto the project for sure, but he did praise his stance on education.

“Senator McCain believes our schools should compete to be the most innovative, flexible and student-centered. He believes we should let them compete for the most effective, character-building teachers, hire them, and reward them,” Mr. Bush said in a statement prepared for The New York Sun. “Under Senator McCain’s leadership, I am confident we will build the world-class learning institutions needed to ensure our students will be competitive in the 21st century global economy.”

A spokesman for Mr. Obama, Hari Sevugan, confirmed that the senator’s staff met with Mr. Klein and Rev. Sharpton yesterday, saying Mr. Obama’s staff also has met with “a large number of education thinkers.”

A deputy chancellor to Mr. Klein who attended yesterday’s meeting with Mr. Obama’s staff, Christopher Cerf, said the project’s effort to recruit political supporters is nonpartisan. “People are very interested in New York’s successes, and we will talk to anybody about them,” Mr. Cerf said. “The rest of the country understands all that we’ve done and is very impressed by it, and we share our philosophies and policies on a nonpartisan basis.”

Ms. Weingarten was also in Chicago yesterday — being elected president of the national American Federation of Teachers, a title she will hold along with her position as president of the city union, the United Federation of Teachers.

Speaking at the union’s national convention in Chicago, Ms. Weingarten yesterday laid out a vision for a revamped federal education law that would promote “community schools.”

She said such schools would serve needy children by incorporating many government services into one building, services that do not just include schooling but medical care, child care, and homework assistance.

Speaking to reporters, Ms. Weingarten said she will begin her work lobbying for an overhauled education law as soon as tomorrow, when she expects to be in Washington, D.C.