Mr. Obama’s advisers appeared almost to expect a different Mitt Romney to turn up for the debate: the hard-edged conservative who had largely pitched his message to the Republican base. Instead, Mr. Romney softened his rhetoric, promising that his reform of Medicare would not touch benefits for older Americans and praising elements of Mr. Obama’s education policy. He also tried to paint the president as a protector of big banks because of the post-financial-crisis government bailout of the banking industry.

Campaign officials said they wished Mr. Obama had called out Mr. Romney on assertions that they said were untrue, although they conceded that some of the weaknesses in the president’s performance were simply part of his approach to debates, which is to shy away from highly personal confrontations. The base wants him “to gut Romney,” one adviser said, but swing voters hate that and the president was trying to find a balance.

Even so, Democrats questioned why he did not bring up a range of issues they considered favorable to Mr. Obama, including women’s rights; Mr. Romney’s taxes; the Republican candidate’s comments about the “47 percent” of Americans who consider themselves “victims” dependent on the government; and the record of his former firm, Bain Capital. Some Colorado Democrats leaving the debate seemed despondent at the president’s performance and fretted that he had put their state back in play.

“The president did well in terms of substance but I think there were opportunities to hold Governor Romney accountable that may have been missed,” former Gov. Ted Strickland of Ohio, a close ally of the campaign, said in an interview. “But you know, it’s one debate. There are two more.”

Other Democrats picked up what they saw as Mr. Obama’s missed opportunities, assailing Mr. Romney for misleading viewers about his tax plan and other issues. The Center for American Progress, a left-leaning organization, posted what it called “27 myths” told in 38 minutes.

A new television ad produced by the Obama campaign for seven swing states showed Mr. Romney denying aspects of his tax plan. “If we can’t trust him here, how could we ever trust him here?” the ad asks as a picture of the Oval Office comes on screen. “He was just lying,” Mr. Strickland said. “He was fast and loose with the truth.” The Romney camp countered with the various ways they asserted Mr. Obama misled about the issues during the debate.

Appearing at his morning rally on Thursday, Mr. Obama seemed more energetic than he had the night before. Clad in khakis and a blue Windbreaker, he mocked Mr. Romney in a way he had not during his sober performance on Wednesday night. He singled out Mr. Romney’s promise to cut funding for the Public Broadcasting System, including its signature children’s character.