Mr. Christie’s strategy of bipartisanship and outreach deliberately echoed that of another Republican governor who seized the White House after eight years of Democratic control: George W. Bush.

“We work together and they don’t,” Mr. Christie said in an interview on Tuesday morning, contrasting Trenton and Washington. “It’s not like we like each other any more than they do. I got plenty of Democrats I don’t like here and that don’t like me. But we’ve made the decision that we’re going to work together.”

In the interview, Mr. Christie said intelligent voices were being drowned out in Washington, and described the effort led by Senator Ted Cruz of Texas to cut off funding for President Obama’s health care program as “a monumental failure.”

The swell of national attention around Mr. Christie had grown in the run-up to Election Day, as network cameras filmed his every move — he had a CNN microphone clipped to his tie as he campaigned on Tuesday morning at the Peterpank Diner in Central New Jersey. His campaign bus had been swarmed by people seeking autographs on photos of the governor at the White House, on the cover of Time magazine, and even with his wife, Mary Pat, on their wedding day. Some clearly hoped to offer the souvenirs later for sale.

Mr. Christie’s national profile will only increase later this month as he assumes leadership of the Republican Governors Association, which gives him sway over which state candidates the party will support, allowing him to rack up favors with other Republicans and create relationships with local leaders in key presidential states.

In the interview, Mr. Christie said he would be appearing frequently in “places like Ohio and Michigan and Florida,” all states with incumbent Republican governors up for re-election next year. He has also told South Carolina Republicans that he wants to help Senator Lindsey Graham, who is facing a conservative primary challenge next year. And in New Hampshire, which has the country’s first presidential primary, the national committeeman, Stephen Duprey, said he was inviting Mr. Christie to the state to discuss policy and to raise money for the party.