During a special closed-door meeting, the United Federation of Teachers voted last night to give the mayor a deadline to finalize a contract with the union.

With pressure mounting from angry teachers who have entered their third school year without a contract, the union passed a resolution calling for the mayor to return to the table and threatened that if an agreement is not reached before the UFT meets in October, it could push for a secret ballot authorizing a strike. A date has not yet been set for the October meeting.

“We are willing to negotiate, we are available 24-7,” the union’s president, Randi Weingarten, told reporters after the meeting in downtown Brooklyn. “But it has to end, so we’ve given the mayor a deadline.”

“It’s illegal for teachers to strike and counterproductive to raise it,” a spokesman for the mayor, Jordan Barowitz, said. “Mayor Bloomberg gave the teachers the largest raise in history and is optimistic that we can agree to another one.”

Under the state, Taylor Law of 1967, public school teachers are forbidden from striking and can face fines and jail time.

The last time teachers walked off the job was in 1975, when, in the midst of a fiscal crisis, the city fired thousands of teachers and crowded 40 to 60 children into each classroom. The union called a strike that lasted five days.

The union is asking the mayor to use a state arbitration panel’s findings issued last week as a “vehicle” to finalize a contract.

That report calls for 11.4% in raises over three years, but teachers are angry about what they say they must give up in exchange. Among other changes, teachers would be required to work 10 minutes longer a day, devote three extra days a year to professional development, and give up their ability to challenge negative evaluations by their superiors.

“I don’t think the teachers had a choice,” a math teacher at La Guardia High School, Joan Budish, said on her way out of the meeting about the vote for the resolution. “Do I agree with it in my heart? No.”

She also said she does not believe the union is yet prepared to conduct a strike.

More than 2,000 delegates attended yesterday’s meeting, which was moved to the Marriott in downtown Brooklyn to accommodate the large crowd. The monthly meetings typically attract about 800 of the union’s 2,900 delegates.

A small but vocal minority pushed the union to immediately call for a strike, and ultimately a large majority of the members raised their yellow cards to signal a “yes” vote in favor of the resolution, attendees said.

After the meeting, some teachers flooded out and launched into vitriolic attacks against both the mayor and the union leadership. Ms. Weingarten described the meeting as a “healthy and vigorous debate.”

Negotiations between the mayor and union reached an impasse in December. Both sides said they would use the arbitration panel’s findings, which were delivered last Monday, to restart the talks. So far, neither party has returned to the table.

With the mayoral election less than two months away, the teachers union has not endorsed a candidate. Reaching a resolution with the union could only bolster Mr. Bloomberg’s chances at the polls, a political analyst, Hank Sheinkopf said.

“It would be better if there was no conflict with the teachers and the teachers union,” Mr. Sheinkopf said. “People would feel even better about Bloomberg’s management skills.”

On the other hand, he said, “No mayor has never not been elected or reelected because he has a conflict with the city’s municipal unions.”

Politics aside, teacher Christine Celentano said she left a cushy school job in Scarsdale to teach at P.S./M.S. 20 in the Bronx simply because she thought she was needed more there.

“If we don’t get a contract, I will leave this city,” she said yesterday. “And I’m sure there will be a flood of teachers following.”