The same-sex marriage measure failed two years ago when a key democrat in New Jersey abstained from voting.
Right now, New Jersey does allow and recognize civil unions. Still, some say that's not enough, because it prevents protections like health care and hospital visitation available only to spouses.
Since the same-sex marriage defeat in New Jersey two years ago, across the Hudson River, with the support of Democratic Governor Andrew Cuomo, New York State legalized the measure last year.
New Jersey's legislative session begins Tuesday, and the bill *could reach republican Governor Chris Christies desk as early as next week.
New Jersey's Republican Governor Chris Christie, however, has said in the past that he does not support same sex marriage and could veto the measure.