"I think what we did in New Jersey proves that's the way to do it," Christie said on NBC's "Meet the Press" Sunday. "The executive needs to lead and then, bring people to the table to forge compromise."
Christie's remarks came as President Barack Obama was set to meet with Republican leaders, Senate Minority Leader Mitch McConnell and House Speaker John Boehner, at the White House Monday in an effort to restart stalled talks on raising the nation's debt limit.
The Democratically controlled New Jersey state Assembly passed legislation Thursday to close a massive budget gap due to the state's pension and health benefit obligations to public employees in a move predicted to save the state more than $120 billion over the next 30 years.
The legislation, which will increase the amount public employees pay for their healthcare and pension plans and end the ability of unions to collectively bargain for their medical benefits, came after months of intense budget negotiations, Christie said.
"And everybody has got to put skin in the game," he said. "I mean I gave on things that I wanted. Obviously the Senate, Democratic Senate president in my state and the Democratic speaker gave on things they wanted and we came to a compromise that didn't violate our principles. And that's the key."
Christie said the president needed to take the lead in the federal effort on debt reduction.
"If you're the executive, you've got to be the guy who's out there pushing and leading," he said. "You can't lay back and wait for somebody else to do it."
"There is no substitute for the three leaders in the room having to look at each other and having to hash this out."