Christie had been in Washington with President Obama and congressional lawmakers, asking for money to rebuild the state after Hurricane Sandy. Also Thursday, he vetoed a bill that would have set up a state-run insurance exchange under the health-care overhaul law.
That, Stewart said, indicated hypocrisy, because Republicans are selective in their reliance on government to help people.
"This is how I part ways with the Republican Party in an enormous way: If you have cancer and you don't have health insurance, that's your Hurricane Sandy," Stewart said to applause from the studio audience.
He added: "For the Republican Party, if it's not something they personally need, it's an entitlement of the 47 percent that are sucking things out of the government. But when they need, there's all the reasons in the world it should be there."
Christie said the health-care exchange was going to exist in New Jersey no matter what - it was just a matter of whether the state or the federal government runs it. But he won't approve the state's involvement, he said, until the Obama administration answers his questions about how much it's going to cost.
"Maybe the difference between the two parties," Christie said, "is that sometimes the Democratic Party feels the only way to address people's needs and wants is for the government to do that."
Parts of the interview didn't air on TV because of its length, but it was to be available online in its entirety Friday morning.
Christie rejected the broad categories Stewart was attempting to lump Republicans into. To applause, he said: "People elect us to get things done, not just bloviate."
Stewart countered by bringing up Christie's propensity for calling lawmakers and constituents names. He cited something Christie said at a town-hall meeting: "Thank you all very much. I'm sorry for the idiot over there."
Christie asked: "You grew up in New Jersey. How many idiots are there?"
Stewart, who grew up in Lawrenceville, concurred, using a word that may be suitable for cable TV but not for newspapers.
Stewart then said he thought the storm "humbled" Christie - and the governor said it had.
Still, Christie vowed to continue to be "very harsh with people I think are out of line and stupid."
"It's Jersey love, Jon," he said. He noted that he has compromised with Democrats in New Jersey even though they "call each other names" beforehand.
Christie and Stewart, both 50 and Jersey-raised men who love the Mets and Bruce Springsteen, had an easy, rapid-fire repartee. Christie was more polite than is usual in combative moments, and he allowed Stewart to talk over him.
Christie's statewide popularity has soared due to his handling of the aftermath of Sandy and his cooperation with Obama. Stewart said that was because "people saw you drop the B.S., drop that part of politics that is destructive."
"And by the way, you keep that up and I think you and Hillary [Clinton] are going to have a hell of a battle in 2016," Stewart said. He added: "The beautiful thing about the Republican Party right now, it is so starved for that type of real leadership."
Christie, reverting to humor, smoothly avoided addressing the 2016 presidential campaign.
"I think it's really unfair by the way, and I get the import of this, that you look at me and say the word starved," the heavyset governor said, drawing hoots of laughter.
Contact Matt Katz at 609-217-8355 or firstname.lastname@example.org, or follow on Twitter @mattkatz00. Read his blog, "Christie Chronicles," at www.philly.com/christiechronicles.