Just five states - Connecticut, Iowa, Massachusetts, New Hampshire and Vermont - allow same-sex marriages. New Jersey offers civil unions that give gay couples the legal protections of marriage but not the title.
Gay rights advocates see the issue as especially urgent, because the window to pass it is closing.
Gov. Jon S. Corzine, a Democrat, says he wants to sign a bill to allow what supporters call "marriage equality." He said Tuesday after the swearing-in of Camden's new mayor that he hopes the bill "can come to a positive conclusion."
But on Jan. 19, he'll be replaced by Chris Christie, a Republican who says he would veto such a bill if it reached his desk. He, like other opponents, say allowing gay marriage would undermine traditional marriage.
Assembly Speaker Joseph Roberts has said his chamber wouldn't vote on the matter unless the Senate did first.
If the bill is to become law, lawmakers do not have much time to act. For it to be signed this legislative session, the bill would have to be approved by both houses of the Legislature by noon Jan.
While it technically could be passed by the new Legislature between then and Jan. 19, that's logistically more complicated.
Codey has not given any signals that the bill has picked up any more support in the Senate, where he has said it would be several votes short of the 21 needed for passage.
State Sen. Loretta Weinberg, a sponsor of the bill, was optimistic about its chances.
"We're looking forward to having everyone stand up and be counted to make sure all the residents of the state of New Jersey have equal rights," she said.
Patrick Brannigan, executive director of the New Jersey Catholic Conference, said he thinks the vote will kill the measure.
"At this time, we are very confident that there are not sufficient votes in the New Jersey senate to pass the same-sex marriage bill," Brannigan said.