Two days after Mitt Romney reignited his campaign with what many voters saw as a winning debate performance, Republicans were struggling once again to find their footing after a positive September jobs report muted the campaign’s main talking point.

Romney and his surrogates reacted to the news that the unemployment rate had dropped below 8 percent with a flurry of new arguments: that the economy is still moving too slowly, that the jobless rate should really be 11 percent if you count all the people who have dropped out of the workforce, and that the recovery will take even longer if President Obama is reelected. Some Republicans even suggested that the numbers had been manipulated by the Obama administration.

Romney, who has centered his campaign on job creation and cast himself as a Mr. Fixit with business experience that could be applied to the larger economy, has frequently cited Obama’s inability to get the rate below 8 percent as a reason that he should not be reelected. But on Friday, the Labor Department reported that the nation had added 114,000 jobs in September and that the jobless rate had fallen to 7.8 percent, the lowest since Obama took office in 2009.

Stumping in Virginia, Romney was forced to recast his attack on the administration’s economic policies by downplaying the positive news on job creation and focusing instead on the pace of growth.

“There was a report that just came out this morning on job creation this last month. There were fewer new jobs created this month than last month,” Romney said at a rally in Arlington County. “And the unemployment rate, as you noted this year, has come down very, very slowly, but it’s come down nonetheless. The reason it’s come down this year is primarily due to the fact that more and more people have just stopped looking for work.”

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Other Republicans sounded a similar theme, acknowledging some good news in the report but saying that the recovery has taken too long because Obama’s policies simply have not worked.

“While there is positive news in today’s report, job creation is far too slow and the unemployment rate is far too high,” House Speaker John A. Boehner (Ohio) said in a statement. “Administration officials said unemployment would be as low as 5.6 percent by now if Congress passed their ‘stimulus’ spending bill — instead, after four years of spending, taxing, and red tape, millions of Americans remain jobless, underemployed, or have simply given up looking for work.”

Obama, whose performance in Wednesday night’s presidential debate was criticized as lackluster and ineffective, seized on the numbers Friday to underscore his campaign message that the country is slowly recovering and that he needs a second term to finish the job.

“This morning, we found out that the unemployment rate has fallen to its lowest level since I took office. More Americans entered the workforce. More people are getting jobs,” Obama said at a rally in Fairfax. “Now, every month reminds us that we’ve still got too many of our friends and neighbors who are looking for work. And there are too many middle-class families that are still struggling to pay the bills — they were struggling long before the crisis hit. But today’s news certainly is not an excuse to try to talk down the economy to score a few political points. It’s a reminder that this country has come too far to turn back now.”

Polls show Americans feel more optimistic about the economy and believe the worst days are in the past. Gallup’s Economic Confidence Index has been trending up for the past month and is close to its highest level in the past four years, and the number of Americans who say the country is on the “right track” has also risen in recent months, according to Washington Post-ABC News polling.

That slightly more upbeat tone is at odds with Romney’s central campaign argument. The Obama administration has been dogged by the nation’s stubbornly high unemployment rate as the economy slowly recovered from the Great Recession. Over the past several weeks, Romney has refocused and simplified his message: If Obama gets reelected, the next four years will be like the last four years.

But the dip below the 8 percent mark gives the Obama campaign a fresh spin on job growth as the president continues to defend his economic record. On the trail in recent weeks, the president had been citing 24 months of job growth as one of his administration’s accomplishments.

“I think it is a significant event in the course of this election. It helps reinforce that Obama’s policies are moving in the right direction,” said Chris Kofinis, a Democratic strategist. “But it is not sufficient enough to seal victory because the winner of this election is going to be the one who understands the anxiety moms and dads out there and paints a picture of how can help make their future better.”

The somewhat surprising drop in the unemployment rate prompted some Republicans to suggest that the Bureau of Labor Statistics somehow cooked the books to boost the president’s reelection chances.

Former General Electric chief executive Jack Welch, a Romney supporter, tweeted Friday morning: “Unbelievable jobs numbers . . these Chicago guys will do anything . . can’t debate so change numbers.”

Rep. Allen B. West (R-Fla.) also embraced the conspiracy theory, posting this on his Facebook page: “Somehow by manipulation of data, we are all of a sudden below 8 percent unemployment, a month from the presidential election. This is Orwellian to say the least and representative of Saul Alinsky tactics from the book “Rules for Radicals” — a must read for all who want to know how the left strategize.”

The Bureau of Labor Statistics is an independent body set up to ensure no interference from the White House, and its numbers are based on surveys of 60,000 households.

On CNBC on Friday morning, Labor Secretary Hilda L. Solis said it was “ludicrous” to suggest the data have been manipulated to boost Obama.

“I’m insulted when I hear that, because we have a very professional civil service organization where you have top, top economists that work at the BLS,” Solis said. “They’ve been doing these calculations. These are our best-trained and best-skilled individuals working in the BLS, and it’s really ludicrous to hear that kind of statement.”

White House spokesman Josh Earnest called the suspicions “utter nonsense.”

“Anybody, any serious person who has any familiarity with how these numbers are tabulated, understands that these are career employees at the Bureau of Labor Statistics that are responsible for compiling and analyzing these numbers and they do that on their own,” Earnest said.

The next jobs report comes out Nov. 2, four days before voters go to the polls to choose a president.

“It is important to point out that these numbers are very volatile month to month. They’re based on small surveys, and this overstates the case. It’s not as strong as the data suggests,” Mark Zandi, chief economist of Moody’s Analytics, said on MSNBC. “But it makes a strong case that the economy is improving.”