According to an associated press, during a question-and-answer meeting, Cuomo said:
"I want to see it become the law of the state of New York and we’re going to take it up this session," adding that he "is working very hard to pass it."
However Cuomo did not always support the LGBT community in the past, I think any supporter is welcome. I mean don't forget that in 2009, this bill legalizing gay marriage in the state of New York failed, so more there are supporters better it is.
Cuomo mentioned the issue in New York of the State address last month: "We believe in justice for all, then let’s pass marriage equality this year once and for all."