ALBANY — After spending much time on the sidelines of one of the most fiercely debated social issues in America, the Democrat-led Assembly within the next two weeks is “very likely” to pass a bill that would legalize gay marriage, according to a senior lawmaker.

Opposition to gay marriage in the Republican-controlled Senate means it’s highly unlikely the bill will make it out of the Legislature this year. For gay rights advocates, Assembly approval of same-sex marriage would be an important strategic and symbolic victory nonetheless, pushing New York closer to becoming the second state in the nation, after Massachusetts, to extend marriage to same-sex couples — and the first to do so through a legislative process.

While Assembly Democrats have been traditionally supportive of gay rights legislation, they have been reluctant to wade into the gay marriage debate and risk retribution from voters.

The election of Governor Spitzer, one of the most prominent supporters of gay marriage in the national Democratic Party, has changed the equation by providing wary lawmakers with political cover.

“I think it’s very likely that we will pass it this session,” the chairman of the Assembly ‘s health committee, Richard Gottfried, said. Mr. Gottfried was the first legislator to sponsor a gay marriage bill. He said a head count taken by the Assembly speaker, Sheldon Silver, showed that the bill has more than the 76 votes needed to pass the chamber.

In late April, Mr. Spitzer put forward a gay marriage bill, fulfilling a campaign promise. In a memo accompanying his program bill, Mr. Spitzer said granting “legal recognition to these relationships can only strengthen New York’s families, by extending the ability to participate in this crucial social institution to all New Yorkers.”

Mr. Silver, an Orthodox Jew who represents a Lower Manhattan district, has not taken a position, saying he is waiting for his colleagues to come to a consensus.

The Republican Senate majority leader, Joseph Bruno, has said he does not support gay marriage and has suggested that attention toward the issue has distracted lawmakers from addressing other issues, such as the upstate economy.

Advocates of gay marriage have focused their lobbying efforts squarely on the Assembly, putting off a lobbying campaign in the Senate for the time being. By getting one chamber to back the measure, advocates hope to isolate the other, putting more pressure on it to take a stance.

The bill’s main sponsor this year is Daniel O’Donnell, an openly gay Democrat from Manhattan. He has sedulously accumulated support for the bill the entire year. “I don’t know whether it’s coming to a vote,” Mr. O’Donnell said. “I think it’s very important for the overall fight for equality that it does come to the floor.”