But Archbishop Timothy M. Dolan, the state’s top Roman Catholic leader, dismissed those protections as insufficient. And he issued his longest and strongest statement yet on the issue, urging lawmakers not to cave to what he characterized as a “stampede” toward legalizing same-sex marriage.

“Last time I consulted an atlas, it is clear we are living in New York, in the United States of America — not in China or North Korea,” he said. “In those countries, government presumes daily to ‘redefine’ rights, relationships, values, and natural law. There, communiqués from the government can dictate the size of families, who lives and who dies, and what the very definition of ‘family’ and ‘marriage’ means.”

But here momentum was clearly building for a vote on same-sex marriage this week. On Monday, Senator James S. Alesi of Monroe County became the first Republican senator to declare support for the bill, joining three Senate Democrats who had voted against the measure two years ago but said they would vote for it this year. On Tuesday, Mr. McDonald told the Republican leadership, the governor and gay-rights advocates that he would support the measure, and then told reporters, “I think I’m doing the right thing, it’s the appropriate thing, and if the public respects that, I’m grateful.”

There are now 31 declared supporters of same-sex marriage in the Republican-controlled, 62-member Senate. The Assembly, which is controlled by Democrats, has voted in favor of same-sex marriage several times and is expected to do so again this week.

The legislation is strongly opposed by the state’s Conservative Party, whose chairman, Michael Long, has said it will not endorse any Republican who votes for same-sex marriage. Republicans hold a bare 32-to-30 majority in the Senate, and rely on the Conservative Party’s endorsement, and the votes that endorsement brings, to win in many swing districts.

Some Senate Republicans thought to be potential swing votes on the issue, like John J. Flanagan of Long Island, said Tuesday that they still planned to vote against the measure.

But several Republican senators who had previously voted against same-sex marriage acknowledged that they were now undecided, including Mark Grisanti of Buffalo and Stephen M. Saland of the Hudson Valley.

Andrew J. Lanza, a Republican senator from Staten Island, said Tuesday that he believed the legislation would pass if brought to a vote. “At this point, if I would vote now, it’s no,” Mr. Lanza said. “I’m trying to determine if that’s where, whenever the vote comes, that’s where I should ultimately be. I’m open to the notion that being a ‘no’ is not the right vote.”