President Obama sought to put a sluggish debate performance behind him Thursday with a pair of combative speeches in swing states, as his campaign advisers acknowledged that he would have to change his approach before meeting Republican nominee Mitt Romney again on a national stage.

Obama advisers said the president decided before Wednesday’s debate that he would not fight his rival before a prime-time television audience. They acknowledged that Obama will have to do more in the next debate to defend his record and hold Romney more accountable for his economic proposals, which the president sharply criticized Thursday on the campaign trail.

But a wave of anxiety rippled through the Democratic ranks, with many of Obama’s supporters suddenly nervous about their candidate with just over a month left before the election. Some leading Democrats played down the debate’s significance. Others offered various explanations — including, from former vice president Al Gore, that Obama had been disoriented by Denver’s altitude after flying in from the Nevada lowlands — for an uncharacteristically poor public performance from the president.

Attempting to regain the upper hand in what is still a close race, Obama appeared Thursday at campaign rallies in Denver and later in Madison, Wis., in a pair of states critical to his reelection efforts. At both events, Obama roundly criticized Romney as misrepresenting himself and his policies during the debate.

“It couldn’t have been the real Mitt Romney,” Obama told thousands of supporters gathered in Denver’s Sloan’s Lake Park, “because the real Mitt Romney has been running around the country all year promising $5 trillion in tax cuts to the wealthy, but the fellow onstage last night did not know anything about that. The real Mitt Romney said we do not need any more teachers in the classroom, but the fellow onstage said he loves teachers, can’t get enough of them.”

Romney also appeared in Colorado, where he described the debate as a “great opportunity for the American people to see two very different visions for the country.” Later he took the stage with his running mate, Rep. Paul Ryan (Wis.), in Virginia.

Obama’s high spirits on the stump the day after the debate — he mocked Romney several times for pledging to “fire” Big Bird by cutting federal funding to public television — belied his listless demeanor of the previous night.

The president’s campaign faced an onslaught of questions about the performance, chiefly: What happened to Obama in Denver? And why hadn’t he said the critical things he did Thursday when he had a television audience of nearly 60 million people watching?

“He made a choice last night to answer the questions that were asked and to talk to the American people about what we need to do to move forward and not get into serial fact-checking with Governor Romney, which can be a tiring pursuit,” David Axelrod, a senior campaign adviser, told reporters.

But Axelrod acknowledged that “I’m sure we will make adjustments,” adding later that “we have to strike a balance.”

“You can’t allow someone to stand there and manhandle the truth about your record and theirs,” Axelrod said.

David Plouffe, a senior White House adviser, told reporters on Air Force One that the president will change his approach for the next presidential debate, scheduled for Oct. 16 in New York. “We are obviously going to have to adjust for the fact of Mitt Romney’s dishonesty,” he said.

For some, particularly members of his party, Obama’s decision not to defend himself against Romney’s sustained criticism — or draw on some of the successful attacks his campaign has leveled in recent weeks — made him appear absent from the contest.

Heading into the debate, campaign officials said, Obama had decided to augment rather than repeat his campaign advertising that has highlighted Romney’s record with Bain Capital and secretly recorded comments he made that disparaged 47 percent of the country as being dependent on the government.

Some instant polls found that Romney came out the winner. Still, it is unclear how his success on the same stage as Obama will translate into new support in a race that has appeared to be tilted toward the president for weeks.

Romney spokeswoman Amanda Henneberg called the defenses of Obama “just like the president’s performance last night.”

“The campaign, like the president, offered no defense of the president’s first-term record or vision for a second term, and instead offered nothing but false attacks, petulant statements and lies about Governor Romney’s record,” she said.

For much of his presidency, Obama has battled an impression that he is an aloof leader, eager to remain above a political process unpopular with much of the country. How willing he is to fight for his policies remains a mystery to some of his party’s leaders.

Often looking down or smiling thinly during a Romney critique, Obama appeared out of sorts for much of Wednesday’s debate, irritated by the attacks and uncertain in his responses to them.

The showing appeared so out of character for an orator of Obama's ability that the theories to explain it Thursday sometimes bordered on the bizarre. Some Democratic supporters offered that the president had been flustered by Romney’s deceit, or that perhaps he had been pacing himself knowing that two more debates remain. Plouffe suggested that the media wanted a Romney “comeback” story, so much so that pundits overplayed Obama’s poor performance.

Presidents often have trouble in their first reelection debates.

After nearly four years in office, they are unaccustomed to being challenged and have a record that their challengers do not. Defensive is often their default position, as incumbents from Ronald Reagan through George W. Bush demonstrated.

“There is a history of presidents in first debates, and I think we fell prey to it,” Axelrod said in an interview. “And Romney is a great actor in a setting like that. That doesn’t come naturally to the president.”

In his earlier conference call, Axelrod emphasized Romney’s “performance” while adding that it was marked by “serial evasions and deceptions.” He cited Romney’s description of his planned tax cuts as revenue-neutral, his assertion that he would replace Obama’s health-care law with a plan that would prevent insurance companies from refusing to cover people with preexisting conditions, and his support for education spending.

“A day after, I think the question for you and for the American people is really one of character,” Axelrod said.

Reinforcing that message, the Obama campaign released a new television advertisement Thursday titled “Trust.” The ad challenges Romney’s contention that his tax-cut plans would not add to the federal deficit, asking, “Why won’t Romney level with us about his tax plan, which gives the wealthy huge new tax breaks?”

“Because, according to experts, he’d have to raise taxes on the middle class — or increase the deficit to pay for it,” the ad says.

Although Obama’s debate performance energized the Romney camp, how many votes it will change is unknown.

A Democratic official, who spoke on the condition of anonymity to discuss the Obama team, said a “dial-in” poll conducted by campaign officials during the debate showed that the president won over more “persuadable” voters than Romney did. The official said that 60 people in a swing state participated in the survey, and that Obama went from a 1 percent lead among them before the debate to 4 percent after it ended.

In Columbus, Ohio, a key state in the race, the debate brought consternation to Obama supporters and reassurance to Romney backers. Few switched sides.

“He was very well-spoken,” Obama supporter Jenna Kaun, 31, said of Romney as she drank a cup of coffee at Pistachio Vera. “But he didn’t go into details.”

Kaun watched the debate with her husband — a rare undecided voter. By the end, she still planned to vote for Obama and he remained undecided. “Romney was on the offense,” she said. But her husband, she said, “wishes Romney had more details.”

Romney supporter Rita Foley, 52, said she listened to the debate on the radio while driving to her daughter’s house.

“I didn’t see a clear winner. They seemed pretty matched,” she said. Yet, Foley said, “then I got to my daughter’s house and she said on TV, Obama looked anxious.”

“It really surprised me,” she said. “I thought he was supposed to be this great debater.”

James Reid, 34, an aircraft mechanic, said he wished that the best ideas of both candidates could be found in a third candidate. For now, the son and grandson of Ford Motor workers from Detroit said he’ll vote for Obama.

“When Romney said ‘Let Detroit go bankrupt,’ he lost my vote at that,” Reid said. “He’s a businessman, and that’s who he’s looking out for.”

Wilson reported from Washington, Nakamura from Denver and Madison, Wis. Rosalind S. Helderman in Columbus, Ohio, contributed to this report.