ALBANY – Two weeks before the state Senate completed its budget proposal, New York’s teachers union swung into action.

At the end of last month, the Republican leadership led by Joseph Bruno announced that it would propose an education tax credit that would be given to parents “for costs of attending another public school, a qualified nonpublic school, or for tutoring.”

For New York State United Teachers, the idea of a tax credit linked to private school tuition was a major threat.

It would be an embarrassing defeat for the union, which fears that the tax credits would open the door to larger tuition programs and would force the public school teachers to compete against private schools for tax dollars.

If the Senate backed the plan, which is favored by Governor Pataki and the Catholic Church, its chances of ending up in the final budget agreement would have increased greatly.

Responding to the Senate’s budget preview, the union spent close to $1 million in an intense lobbying campaign that targeted the most vulnerable Republican lawmakers. The effort included a $750,000 television spot that ran across the state and featured a slow-motion montage of people, including a little girl on the brink of tears and a somber African-American family, waving goodbye “to the money that our public schools need.” Union leaders organized a phone bank operation to get members to swamp lawmakers with telephone calls and faxes.

“I think the turning point was when our members started reaching out to their senators,” the executive vice president of the union, Alan Lu bin, who oversees its political organizing, said.

On Monday, the Senate came out with a dramatically different tax credit plan, one that the state teachers union and the United Federation of Teachers in New York City say is far more acceptable. The Senate, in its revised proposal, severed the link between the tax credits and private school tuition by not restricting how parents are allowed to use the credits. Parents would receive a $333 credit for every child attending school.

“I think Bruno is very responsive to the members of the conference,” Mr. Lubin said in a telephone interview.

The Senate’s change in position, political observers said, points to the reality facing the tax credits’ primary proponent, the Catholic Church: that the teachers unions are a more experienced and better organized interest group. The unions have an “arsenal available to them to oppose this,” said James Cultrara, the director for education at the New York State Catholic Conference, the public policy branch of the Catholic Church in New York. “And it’s a daunting task to advance a proposal that they oppose. … The church is a church. We’re in the business of faith.”

Senator Nick Spano, a Republican of Westchester County who won his last election by a slim margin, was among members of the conference who had urged the Senate to oppose the original plan involving tuition. “Rather than get involved in a great deal of controversy and national debate,” he told The New York Sun, “let’s provide the taxpayers what they need in New York State, and that’s tax relief.”

Mr. Spano said the Senate’s proposal is a reflection of its “partnership with labor in the state that is unique for Republicans.”