Republican presidential hopeful Rick Perry spent much of Thursday trying to contain the damage from his debate-night debacle here on Wednesday by poking fun at himself, promising to press on and playing down the value of oratory skills.

“We’ve got a debater in chief right now that’s not working out so well,” said the Texas governor, taking a shot at President Obama’s public-speaking talents. “We’ve got to focus on the substance of what’s killing America, and it’s Washington, D.C., spending too much money and creating too much debt.”

But even as the Perry rehabilitation tour went into full swing, Republicans inside and outside his campaign were skeptical of his prospects for survival.

“We’re in one of those stop-the-fights, throw-in-the-white-towel moments,” said Alex Castellanos, a Republican consultant who supported Mitt Romney in the 2008 presidential race but is not affiliated with any of the 2012 campaigns. “It was just brutal. It turns out that being president is a very hard job. I think Perry’s taken himself out of consideration now.”

Perry began Thursday with a whirlwind tour of morning talk shows and moved on to “Late Show With David Letterman” in New York, making light of his gaffe and trying to combat the perception that his series of debate stumbles makes him ill suited for the rigors of a presidential campaign.

Although many Republicans praised Perry’s handling of the situation, most said it was not enough. Dozens of Republicans who were interviewed for this article, but who spoke on the condition of anonymity to discuss the campaign freely, observed that the governor will have great trouble attracting the new donors and supporters he already needed to turn around his campaign.

Some of Perry’s backers rushed to his defense. Louisiana Gov. Bobby Jindal, one of his most prominent surrogates, issued a statement that said Perry is still “the right person” to defeat Obama. “He’s got a strong track record in Texas, and he knows how to create jobs and get America working again,” Jindal said.

Reaction to the gaffe, which took place during a televised debate in the Detroit suburbs, came on a day when the intensity of the GOP presidential contest notched up considerably, with less than two months until voting begins in the early-nominating states.

With another debate scheduled for Saturday in South Carolina, the two front-runners in the field — Romney, a former Massachusetts governor, and Georgia businessman Herman Cain — remained in Michigan for a busy day of retail politicking.

Romney, rallying a couple of hundred supporters a few miles from the Detroit suburb where he grew up, ducked questions about Perry’s performance, saying only that he was pleased with his own performance. “I’ve got to worry more about me than anybody else,” Romney said.

Cain, mingling with supporters in Ypsilanti, Mich., tried jovially to move past the sexual harassment allegations that have consumed his presidential campaign by training his attacks on Obama.

“How do you beat Obama? Beat him with a Cain,” he quipped at the Big Sky Diner.

The Cain campaign announced that it had raised more than $9 million in the past six weeks.

But it was Perry’s unforced error onstage at Oakland University here Wednesday night that seemed the most crucial development of the day. The Texas governor appeared to draw a blank as he tried to recall the third of three federal agencies he would abolish if elected president.

“It is three agencies of government when I get there that are gone,” he said, beginning to lay out one of the staples of his stump speech. “Commerce, Education, and the — what’s the third one there? Let’s see,” Perry said.

“Commerce and, let’s see,” he continued. “I can’t. The third one, I can’t. Sorry. Oops.”

The episode prompted a grim examination among friends and rivals of whether a path to victory still exists for him. Many Republicans, particularly those aligned with the campaign, spoke on the condition of anonymity to discuss the matter freely. They said Perry’s challenge goes beyond whether he can gain more financial backers to his ability to attract new voters at all.

“It was a totally sick-to-my-stomach feeling. I just wanted to crawl under the table and hide,” said one Republican strategist who is not aligned with a campaign. “Nothing is impossible in political campaigns. But this is going to be very, very difficult. There’s just going to be a large percentage of the electorate that’s going to think he isn’t ready for the job.”

One adviser acknowledged before the debate that the candidate understood he needed a “mistake-free” week to turn his fortunes around. He didn’t get one.

But the Perry campaign insisted that the moment was not fatal.

“The good news after this roller-coaster nomination season . . . it’s clear that voters are open to looking at candidates more than once, and they are still shopping,” senior strategist Dave Carney said by e-mail Thursday. “Most Americans understand that some candidates are human. Rick Perry is authentic, human, and consistent. His record and his ideas will trump Obama next fall.”

Still, Perry’s blunder prompted speculation about whether he has made the path to victory too difficult for himself. His initial resistance to entering the race — and his late decision to do so in part at the urging of his wife, Anita — has fed a perception that he has always been a reluctant contender.

Perry’s struggles have called attention to the reality that, although popular in Texas, he is politically untested outside the safe waters of a strongly Republican state, and the late entry deprived him of the opportunity to discover and work on his weaknesses away from the glare of a campaign that was already fully in swing.

Perry excels in one-on-one interactions, several Republicans said. He never forgets a name. If he had more time to show that side of himself to voters, his chances may look a little better now, they said.

“When he came out to Indiana, his prepared marks were subpar, but his Q&A with our chairman was awesome,” said Pete Seat, who was a White House spokesman under President George W. Bush and is now with the Indiana Republican Party. “Retail is where he excelled. But he’s backed into this corner. His only choice is to turn in one or two good debate performances. You’re not going to move numbers where he needs to move them just by shaking hands.”

Staff writers Chris Cillizza, Dan Balz, Dan Eggen and Karen Tumulty contributed to this report.