State Sen. Barbara Buono made the call as she gathered with fellow Democrats outside the home of a lesbian couple, The New York Times reported Tuesday.
Democrats need only three Republican votes to override Christie's veto of a same-sex marriage bill. Some GOP legislators have indicated they would vote for the override, but fear retribution from Christie, who is known as a party disciplinarian.
"One man in New Jersey stands in the way of marriage equality," said Buono, who is challenging Christie in the November gubernatorial race. "The time is now -- the time is now for this governor to step out of the way of progress."
Christie has termed as "insulting" last week's ruling by the U.S. Supreme Court that gays and lesbians had the right to marry.
The governor has said he would not oppose same-sex marriage if New Jersey voters approved it in a statewide referendum.
Polls show about 60 percent of the state's voters support the right of gays and lesbians to marry.