DENVER—President Barack Obama, stung by bad reviews in his first debate of the 2012 White House race, joked Thursday that the "very spirited fellow" onstage with him was "not the real Mitt Romney." Obama also mocked the former Massachusetts governor's pledge to cut government subsidies for PBS as "finally getting tough on Big Bird."

"When I got onto the stage, I met this very spirited fellow who claimed to be Mitt Romney," he told cheering supporters here. "But it couldn't have been Mitt Romney, because the real Mitt Romney has been running around the country for the last year promising $5 trillion in tax cuts that favor the wealthy."

"The fellow onstage last night said he didn't know anything about that," Obama said. The president then gave the same treatment to Romney on education and other issues—and hit back at one of Romney's debate zingers, "I maybe need to get a new accountant," uttered in a spat about outsourcing and whether companies can take a tax deduction for shipping jobs overseas.

"We know for sure it was not the real Mitt Romney because he seems to be doing just fine with his current accountant," Obama said.

Obama's wry comments—belated comebacks to criticisms Romney leveled the night before—came as a top aide told reporters the president's campaign would likely make "adjustments" to its approach to future debates.

The president also riffed on Romney's vow to rein in government subsidies for things like PBS. Romney said at the debate that "I like PBS. I love Big Bird. ... But I'm not going to keep on spending money on things to borrow money from China to pay for it."

"Thank goodness somebody is finally getting tough on Big Bird," Obama said at the Denver rally. "We didn't know that Big Bird was driving the federal deficit." Someone in the crowd shouted, "And Elmo!" "Elmo too?" Obama said with a smile.

DJ will.i.am tried to set the mood before the president spoke, playing a song touting "a new day" and a remixed version of Journey's karaoke favorite "Don't Stop Believin'" as the crowd in Sloan's Lake Park sang along. Some 12,300 people turned out to see the president, according to a city and county of Denver official.

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"A lot of us came out here because of last night, to let him know 'Don't worry, we're still here,'" said Mary-Ellen Turner, a 64-year-old homeopath wrapped in a green sleeping bag for warmth in the morning chill. "But it's good for us too."

"This makes me feel better after last night, you know. Seeing all these people out for the president. I was worried, I'll tell you," said Jack Walker, 76, a retired Greyhound bus driver.

Turner and Walker, who said they met in line, were unhappy and unsettled about Obama's subdued debate performance.

"I thought he should have attacked him [Romney] more, been more assertive," Walker said. "I don't know, maybe it'll all work out."

"I really hope that was a strategy to make Romney look like the bully he is, an attack dog. But I don't know if that's what really was going on," Turner said.

Democratic Sen. Mark Udall told the crowd that Obama had been "thoughtful, dignified, substantive and truthful." "He told us what he's for," Udall said, as the crowd cheered.

Udall later told reporters that the Obama campaign's energy level was "a little low this morning." "But campaigns are peaks and valleys," he added with a shrug.

Later in the day, Obama redoubled his attack at a rally in Madison, Wis., that drew some 36,000 people.

"I just want to make sure I got this straight. He'll get rid of regulations on Wall Street, but he's going to crack down on Sesame Street," Obama said. "Thank goodness somebody is finally cracking down on Big Bird. Who knew that he was responsible for all these deficits? Elmo has got to watch out."

Top Obama campaign strategist David Axelrod talked to reporters on a conference call Thursday about the fight going forward, saying "we're going to take a hard look at this" and "I'm sure we will make adjustments."

"He may win the Oscar for his performance last night, but he's not going to win the presidency for his performance last night," Axelrod insisted. Romney's strong showing, he said, "can't make up for the gap" in battleground states that will decide the election.