"I think there's gotta be a solution other than that," Christie said in an interview that will air on CBS' "Sunday Morning" this weekend.
The governor suggested that Republicans pushing for a shutdown were acting recklessly.
"Quite frankly, to be fair, I don't think you hear responsible Republican leaders advocating a shutdown of the government," Christie said. He noted that a shutdown, "by definition, is a failure."
"You gotta work it out," Christie said. "They'll work it out this week, I'm confident they will, because I don't think anybody wants to go down that road."
The looming government shutdown has been especially divisive for Republicans opposed to Obamacare. Christie has accepted key components of the Affordable Care Act for New Jersey, but has spoken adamantly against the law and has campaigned for candidates committed to repealing it.
The CBS interview was the first time Christie addressed whether he'd fight Obamacare to the point of letting the government shut down.
"He is either unwilling or unable to speak up against these guys," Democratic National Committee spokesman Mike Czin said of Christie.