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“I’m going to play music to bring the energy up,” he said. “I know people are low. It’s cold. But there’s a fire right here within us.”

Former Denver Mayor Federico Pena said he was “very proud” of Mr. Obama’s presentation in the debate.

“The president spoke the truth, and the truth counts,” he said. Mr. Pena referred to the Republican as the “new Mitt Romney” for his supposed newfound support for the middle class.

The next presidential debate will cover foreign policy, and some of Mr. Obama’s thoughts Thursday were already on what his opponent might say or do.

“It will be interesting to see what the guy who was playing Mitt Romney yesterday will say about foreign policy when we meet next, because he said it was ‘tragic’ to end the war in Iraq,” Mr. Obama said. “He won’t tell us how he’ll end the war in Afghanistan.”

Mr. Romney’s strong performance also adds pressure to Vice President Joseph R. Biden, who squares off against Republican vice presidential nominee Paul Ryan next week in Danville, Ky.

Mr. Biden told reporters that Mr. Obama “did well” and was “presidential” against what he described as his shifting Republican rival. Mr. Biden said he is studying the finer details of Mr. Ryan’s positions so the Wisconsin Republican can’t follow Mr. Romney’s example and easily pivot away from attacks.

“You just don’t ever know what game, what positions Gov. Romney’s going to come with,” he told reporters while campaigning in Iowa. “Last night, we found out he doesn’t have a $5 trillion tax cut. I guess he outsourced that to China or something.”

• Susan Crabtree in Washington contributed to this report.