DC needs a pizza party to mend fences: GOP pro

Mending fences on Capitol Hill? Start with the pizza: Pro

The first thing Republicans and Democrats need to do is rebuild goodwill and "get to know each other" again following the latest bruising debt fight, former White House budget director Jim Nussle told CNBC on Friday.

"Let's start with the pizza" and then get down to the work to find solutions to the nation's debt problems, said Nussle, who served as director of the Office of Management and Budget under President George W. Bush.

Nussle spoke on "Squawk Box" a day after President Barack Obama challenged Republicans to "win an election" if they want to overturn his policies.

(Read more: 'Win an election': Obama catchphrase)

Despite the tough talk, "the president is totally capable of negotiating" with Republicans, said Steven Rattner, who served as Obama's car czar.

This week's eventual compromise to extend the debt ceiling until Feb. 7 and reopen the government with funding until Jan. 15 was a "teachable moment," he said. "I think we have learned the American people do not believe in using the debt ceiling as a negotiating tool."

"The American people have [also] said, 'no mas,' to trying to get rid of Obamacare through the back door," said Rattner—referring to Republican attempts to use the debt ceiling and the government shutdown as leverage to defund or delay the president's health-care law.

(Read more: Did Wall Street make the next budget crisis worse?)

With a three month reprieve, Rattner and Nussle, members for the Campaign to Fix the Debt, believe the elusive "grand bargain" is worth pursuing, despite sentiment in Congress against it.

(Read more: Grand Bargain' probably won't happen: John McCain

Nussle said that budgeteers each need to come to the negotiating table with a plan of their own. "There is a no deal until there's a deal on everything."

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But Rattner pointed out, "There's no enforcing mechanism. There's no super committee. There's no sequestration [spending cuts] on the back end. You got nothing to make these guys do it."

"Forget the question about what you think the deficit should be," he said. "If you simply look within spending, our priorities are all completely misguided."

He added that "we're cutting all the wrong things," while the tax code is "riddled with loopholes."

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.