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Mr. Cantor noted that Erskine Bowles, the Democrat who ran Mr. Obama’s deficit commission two years ago, said he sees no serious conversation about tackling budget-busting entitlement programs such as Medicare and Medicaid.

“This has to be a part of this agreement, or else we just continue to dig the hole deeper, asking folks to allow us to kick the can down the road further, and that we don’t want to do,” Mr. Cantor said.

The president said he hopes that both parties will agree on the framework of a debt-cutting deal by Christmas.

Mr. Obama, who last met with congressional leaders about the looming “fiscal cliff” on Nov. 16, tried to assure the public that he’s working hard on the problem.

“I want to assure the American people I’m doing my part,” he said. “I’m sitting down with CEOs; I’m sitting down with labor leaders. I’m talking to leaders in Congress. I am ready and able and willing and excited to go ahead and get this issue resolved in a bipartisan fashion so that American families and American businesses have some certainty going into next year.”

Noting that he is traveling to Pennsylvania on Friday to rally public support for his position, Mr. Obama said, “I’ll go anywhere and I’ll do whatever it takes to get this done.”

He said that if Congress first resolves the issue of tax cuts for the middle class, “a lot of the other stuff is going to be a lot easier” to resolve in the new year.