The governor, a Democrat, is expected to introduce the bill on Thursday -- reviving a bill that died in 2007.
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The gay marriage movement has gained momentum in the past two weeks after legislators in Vermont overrode the governor's veto of a gay marriage legalization bill and the Supreme Court in Iowa's ruling that gay couples have the right to marry.
A spokesman for Senate Majority Leader Malcolm Smith says he doesn't believe there are enough votes in the chamber to pass the bill.