Alesi announced his support for the bill last week, the first Republican to do so. He had previously voted against marriage equality in 2009 when it failed to pass the state Senate.
"Passing marriage equality is the most important thing that I think I can do in my 20-year history as a legislator," Alesi said.
Referring to the order votes would be cast (which is alphabetical), Alesi added: "I am proud to be a Republican. I will also be proud to be the first Republican voter to vote for marriage equality in this state."
Watch, via the Capitol Confidential blog of the Times-Union:
The Republican controlled Senate is still debating whether to bring the bill up for a vote, which passed out of Assembly last week. Some members of the caucus are pushing for more specific exemptions for religious groups.
Though the legislative session technically ended Monday, it was extended because of the marriage equality bill, as well several other unresolved issues including a deal on extending rent regulations.
Republican Majority Leader Dean Skelos said Tuesday that a deal on the other legislative matters is close to being reached, though he reiterated that there is still no deal on marriage equality. "Most of those issues I think we're going to resolve very shortly," he said. "We're working on the details, but I am very confident that between the governor -- and he has shown tremendous leadership once again -- and the speaker, showing flexibility, that we will have a session completion by tomorrow."