“What the governor is attempting to do is create a myth of inevitability,” said Brian Brown, the president of the National Organization for Marriage, which is planning a flurry of TV advertisements in Republican districts and coordinating 500,000 telephone calls to Republican senators in the coming days.

“I don’t think the votes are there,” Mr. Brown said.

The lawmakers who endorsed same-sex marriage on Monday included Senator James S. Alesi of Monroe County, who is the first Republican to voice support for the measure. Mr. Alesi’s announcement came shortly after three New York City Democrats, Joseph P. Addabbo Jr. and Shirley L. Huntley, both of Queens, and Carl Kruger of Brooklyn, declared their support.

Mr. Alesi informed Mr. Cuomo of his decision in a meeting on Monday afternoon. Speaking to reporters afterward, Mr. Alesi said he had anguished over his earlier opposition, and had apologized to gay-rights advocates “for voting politically rather than in a way that in my heart and soul I felt I should have voted.”

“What it really comes down to is one word: It’s equality, which is a basic right of living in America,” Mr. Alesi said. He qualified his support, saying he would vote for the bill only if it included protections for religious institutions.

All four senators who switched their votes said they had been persuaded to do so after discussing the issue with constituents and Senate colleagues in recent months.