The governor - who endorsed Clinton in April and campaigned for her in many states - reiterated his support for her. However, he added that if she lost in Ohio and Texas "then I think the time to move on probably is at hand."
Both those states will hold their primaries a week from Tuesday.
Corzine said he does not believe the race between Clinton and Illinois Sen. Barack Obama was over, even though Obama has won 11 straight contests and recently grabbed the overall delegate lead.
The governor cited the April primary in Pennsylvania as another important contest and the ongoing disputes over whether delegates from Florida and Michigan should be counted. The Democratic Party stripped the latter two states of their delegates for holding early primaries, though Clinton won both.
Corzine's remarks echo those of former President Bill Clinton, who has said his wife probably needs to win both Ohio and Texas if she's to win the Democratic presidential nomination.
"Those of us who are supporters of Sen. Clinton believe and feel pretty positive about what's going to happen in Ohio and Texas. Our read is that she's doing well; she turns that momentum around if she does well there," Corzine said.
No matter the outcome, Corzine predicted New Jersey would back a Democratic presidential candidate - as it has every election since 1988.
"There's a lot of enthusiasm about both candidates in our state, and I think Democrats are going to do very, very well in New Jersey in the fall," Corzine said.
Corzine discounted the affect of Ralph Nader's independent presidential candidacy, which Nader announced on Sunday. However, Corzine said a potential candidacy by New York Mayor Michael Bloomberg could prove interesting.
"I think that would have major impact on the outcome of the race, and I think it's unpredictable which side would be hurt the most on that," Corzine said. "But that's a question that's much more relevant, I think, to the end game of who the next president of the U.S. is."
