"We had the same kind of situation a year ago, and I just got in the room with the Democrats in the legislature, and we came to a principled agreement," Christie said. "I have a particular message for the president: He should get in and lead and bring them together."
Christie said that no matter the differences, a government shutdown is unacceptable.
"Shutdown is a failure of everybody, including the president. Because in the end, we're here to stand up for principles, to say the things that we believe in, but we're also here to lead and run a government," Christie said. "It would be a failure of everyone involved, of the Congress and the president, if they don't get this done."
Christie, who has an outsized frame to match his bold personality, has recently begun to slim down. With the help of a trainer, he's exercising several times a week and says he has lost weight, though he won't reveal a number.
"Let's just say this -- I feel better, I have more energy, and my wife's happier because, you know, we've got four kids," Christie said.
"What do you say to psyche yourself into it?" Sawyer asked.
"I just look in the mirror, Diane, and I go, 'Okay, I've got to get healthier,'" Christie said. "This job has really forced me, because it's such a draining job from an energy perspective... If I want to be good, I've got to do this."
Christie, born and raised in the Garden State, is also a huge fan of Bruce Springsteen, but the musician and Jersey icon hasn't been shy about criticizing his fan.
Springsteen, who declined to play at the governor's inauguration, recently wrote to a New Jersey newspaper saying that Christie's policies favor the wealthy.
Christie's "cuts are eating away at the lower edges of the middle class, not just those already classified as in poverty, and are likely to continue to get worse over the next few years," Springsteen wrote.
"Are you surprised to hear that from Bruce? I mean, you know, Bruce is liberal," the governor said. "Doesn't mean I like him any less."
Christie's direct, even confrontational nature has certainly grated on some, even as its drawn him millions of fans who click on YouTube videos of the governor berating teachers that he says have disrespected him at town halls.
For his part, Christie says he's determined to defend his positions, stridently if need be.
"If you treat me with respect even when you disagree with me, I'll treat you with respect back. You treat me with disrespect, that's what you're going to get back," Christie said.
"I kind of wake up every morning excited to get going and to get to work," he continued. "Cause the things that we're working on are so important. And I have a chance to actually do something, not just talk about it, but actually do it."