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He also accused Mr. Obama of scuttling a 2011 deal that could have raised some taxes and cut spending, which could have set the country on firmer fiscal footing.

“This isn’t about me and frankly, it’s not about Republicans,” Mr. Boehner said. “This is about saving the future for our kids and our grandkids, and the only way this is going to happen is to in fact have a conversation.”

The president did cheerlead occasionally, calling the U.S. “the one indispensable nation.” But he said the U.S. is losing face internationally due to the shutdown and debt crisis, and referred to his absence at the Asia summmits, where he had hoped to close a trade deal.

“I’m sure the Chinese don’t mind that I’m not there right now,” Mr. Obama said. “I should have been there.”

Could he reassure other nations that the U.S. won’t default on its obligations? Mr. Obama’s answer was a qualified yes, but he also raised doubts about whether his own word was any good.

“Obviously my message to the world is the United States always has paid its bills and it will do so again,” Mr. Obama said. “But I think they’re not just looking at what I say; they’re looking at what Congress does. And that ultimately is up to Speaker Boehner.”

And Americans don’t usually hear their president apologize for the state of affairs, but Mr. Obama did that, too.

“To all the American people, I apologize that you have to go through this stuff every three months, it seems like. And Lord knows I’m tired of it,” the president said.