The governor, who is Roman Catholic, has said that while he does not support same-sex marriage, he would not stand in the way if the state’s voters passed a referendum in favor of it.

But ballot initiatives on gay rights have overwhelmingly failed, aided by national groups that have run campaigns against them. And Democrats here have said that they do not want to put a civil rights matter on the ballot.

State Senator Loretta Weinberg, the leader of the Democratic majority, noted that while the governor accused the courts of legislating same-sex marriage, in New Jersey, the Legislature had actually done so, only to be overruled.

“The only one who is legislating right now is the governor himself,” Ms. Weinberg said.

The Democrats said that they would not schedule the vote on an override — they have until January to do so — until they were confident they had the votes.

They came to this central New Jersey suburb to announce their plans because it is represented by Tom H. Kean Jr., the leader of the Republican minority in the Senate. The couple, Liz Flanagan and Nancy Wilkinson, with their son and two grandchildren standing behind them, told how they met and joined in a civil union, but would be denied benefits of inheritance and health care because they are not married. (“Nice job, Mom,” their son called as Ms. Wilkinson finished.)

“This is embarrassing that people that love each other have to beg us and our colleagues on the Republican side of the aisle to do the right thing,” said Steve Sweeney, the Senate president.

Senator Ray J. Lesniak recalled that as governor, Mr. Kean’s father vetoed a bill requiring a moment of silence in New Jersey schools but urged his fellow Republicans to vote according to their consciences in attempting an override, which succeeded.