The (Newark) Star-Ledger said the state Assembly is expected to take up the bill Thursday.
Two Republicans -- Sen. Jennifer Beck of Monmouth and Sen. Diane Allen of Burlington -- voted yes on the bill, the newspaper said. Two Democrats -- Sen. Ronald Rice of Essex and Sen. Jeff Van Drew of Cape May -- voted no.
The Senate would need 27 votes to override a Christie veto.
The Star-Ledger said Christie wants to put the issue of same-sex marriage before New Jersey voters in November.