Mitt Romney’s challenge, with less than five weeks until Election Day, is to convince voters that the steady, decisive, in-command competitor who showed up for the first presidential debate is the real Mitt Romney.

The Romney whom viewers saw next to President Obama on Wednesday night is not the candidate they’ve come to know through many months of attack ads and replayed gaffes.

The Republican nominee’s team labored Thursday to ensure that his debate triumph was not fleeting, hoping that it could serve as a jolt to his flagging campaign. As one adviser said, “The afterglow will be short-lived.”

Romney is rolling out a new batch of television ads in battleground states, focused on taxes and jobs, that amplify his core argument from the debate: that the country cannot afford another four years of an Obama presidency and must choose a new path.

Aides said that in coming days, Romney won’t merely condemn the $5 trillion in new federal debt amassed during Obama’s term, but also trumpet forecasts that the debt would grow to $20 trillion by the end of a second Obama term.

Advisers said forthcoming ads, as well as public appearances by the candidate and his surrogates, will seek to reinforce Romney’s readiness to be president, something that Democrats and some Republicans had questioned in recent weeks.

The strategy calls for Romney to highlight his connection to “real folks” by sharing anecdotes about voters he has met on the campaign trail. A greater effort will be made to radiate the confidence of someone prepared to sit in the Oval Office.

Even as he finds his footing on the economy, Romney plans to give a major foreign policy speech on Monday at the Virginia Military Institute in which he is expected to challenge Obama’s leadership in the Middle East. Romney’s strategists say the president is becoming more vulnerable on his handling of the tensions in the region.

“He needed a moment where the door was cracked open and now he’s got to put his shoulder to it and go through,” said Terry Holt, who was a strategist on George W. Bush’s campaigns. “People want to see Mitt Romney roll up his sleeves and show how he will go to work. This is an opening, but it will take a steady, determined and focused effort to get this narrative back on firm footing.”

At campaign headquarters in Boston, advisers held briefings with supporters, surrogates and allies in Washington’s chattering class to hammer their message that the election will be a choice between two different paths for the nation, while playing down any expectations of an immediate shift in the race.

On the private briefing calls, pollster Neil Newhouse stressed that although Romney’s debate performance put him on a positive trajectory, it is unlikely to dramatically move numbers in states such as Ohio, where the latest polls show Obama with a significant advantage, according to an adviser also on the calls.

“I don’t think it’s going to be decided by debates alone,” said Eric Fehrnstrom, a senior adviser to Romney. “I think it’s going to be decided by the question voters are going to ask themselves, which is, ‘Do I want another four years like the last four years?’ And on that basis, I think Mitt Romney’s going to win.”

Stuart Stevens, Romney’s chief strategist, who for weeks has been under fire as the campaign struggled with its message and slipped in polls, said Romney is staying focused on the core rationale of his candidacy: that he can turn around the beleaguered economy.

“Listen,” Stevens said, “it’s not that the president had a bad debate. I think he had a bad four years. And he seems to have an inability to come to grips with it and explain why there’s 23 million people looking for work, why there’s 15 more million people living on food stamps, why one out of six Americans are in poverty.”

The next monthly jobs report, expected Friday, could underscore Romney’s argument or provide proof for the more optimistic outlook that Obama and former president Bill Clinton have been espousing.

Obama’s campaign aides said Romney made a series of statements on the debate stage that distorted the truth and could come back to haunt him.

“When I got onto the stage, I met this very spirited fellow who claimed to be Mitt Romney,” Obama said at a Thursday rally in Denver. “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.”

The Romney campaign reported receiving more than two donations every second online Wednesday night, while Romney’s wife, Ann, e-mailed supporters to say, “Seize this day and donate.”

On Thursday afternoon, the candidate called the volunteer who made the campaign’s one-millionth door knock in Ohio. And at Romney’s Ohio headquarters in Columbus, volunteers staffing the phone bank incorporated the debate into their message.

“Are you undecided? Well, you saw the debate last night, didn’t you?” Sheila Oxsher, a volunteer who has made more 10,300 calls to voters this year, asked one.

“Did you get to see the debate?” Oxsher asked another voter, a Republican. “It sure was uplifting, wasn’t it?”

As uplifting as the debate was for Romney’s supporters, campaign advisers acknowledge that he received some helpful breaks. The president did not attack him as he has on the campaign trail, nor did he bring up some of the issues on which Romney has been most vulnerable — such as his remark to wealthy donors at a private fundraiser that the 47 percent of Americans who support Obama are freeloaders who don’t pay federal income taxes, consider themselves “victims” and don’t take responsibility for their lives.

The forum also ignored immigration and hot-button social issues — areas where Romney’s conservative positions might have alienated independent voters. Instead, the Republican was able to strike a moderate, almost populist tone, in part by emphasizing his bipartisan work as governor of Massachusetts.

Romney embraced the universal health-care law he championed and signed in Massachusetts, for instance, and said he would not lower taxes for the wealthiest Americans.

“He seemed more independent, a man with his own mind, not a product of any particular political ideology,” Holt said. “He looked like a competitor reaching for the brass ring. He wanted to win.”

Rosalind S. Helderman in Columbus, Ohio, contributed to this report.