Missouri Gov. Jay Nixon (D), left, speaks at the Special Committee on Homeland Security and Public Safety panel as Virginia Gov. Robert F. McDonnell and Nevada Gov. Brian Sandoval, both Republicans, listen at the National Governors Association winter meeting in Washington on Sunday. (Jose Luis Magana/AP)

As the Republican presidential candidates dig in for a protracted battle for their party’s nomination, GOP leaders are increasingly eager to put the intraparty arguments behind them and focus their attention on defeating President Obama in November.

Republican governors attending the winter meeting of the National Governors Association here this weekend cautiously expressed the hope that the scars from a nomination battle that has turned increasingly personal will heal quickly once there is a nominee. But they said the time and money spent by the candidates attacking one another are resources that would be far better aimed at Obama and the Democrats.

Virginia Gov. Robert F. McDonnell, a supporter of former Massachusetts governor Mitt Romney, said he wishes that his candidate could wrap up the nomination by Super Tuesday, March 6.

“The longer it goes on, the longer money has to be spent against a Republican as opposed to President Obama,” he said, “the more fodder there is for the record for pundits through the fall and the Obama campaign — that’s certainly true. So, yes, a more immediate resolution is clearly preferable.”

Wisconsin Gov. Scott Walker, who has not endorsed anyone but thinks Romney will emerge as the nominee, said he worries that a protracted fight could result in side issues, rather than economic messages, defining the party and the eventual candidate.

“Any day they’re not talking about the economy is a wasted day in terms of contrasting with the president,” he said.

Indiana Gov. Mitch Daniels said the president remains highly vulnerable because of the economy, despite some recent improvements. Once the GOP contest is over, he said, the Republican nominee will have plenty of opportunities to make his case.

“I think a lot of the miniature issues and squabbles and supposed stumbles of today will be long forgotten,” he said.

The governors were gathered days ahead of crucial primaries in Michigan and Arizona. Romney predicted Sunday that he would win both contests over former senator Rick Santorum (Pa.) but also suggested that there will be no quick conclusion to the nomination battle.

“I’m convinced I’m going to become the nominee, and we’ll be willing to take however long it takes to get that job done,” he said on “Fox News Sunday.”

Although Michigan is his native state, Romney fell behind Santorum there immediately after the former senator won three contests on Feb. 7. Romney has staged a significant comeback, with polls showing him in either a dead heat or slightly ahead. In response, Santorum has escalated his attacks on Romney and has vowed to keep the campaign going as long as possible.

Santorum, on NBC’s “Meet the Press,” said his message is resonating in Michigan and described his rival’s economic prescriptions as “sort of warmed-over pabulum . . . ideas that are timid, ideas that are institutional, insider” and designed by Washington lobbyists. “It’s not inspiring anybody,” he said.

Santorum’s best hope Tuesday is in Michigan. He acknowledged that he is trailing in Arizona, saying the state is more difficult demographically for him — setting up the possibility of twin defeats Tuesday. But he added that the results will show “that this is a two-person race right now.”

Appearing on ABC’s “This Week,” Santorum also stood by his comment Saturday that Obama is a “snob” for saying he wants all young people to attend college. He said many people “have no desire or no aspiration to go to college because they have a different set of skills and desires and dreams that don’t include college,” and to suggest otherwise “devalues the tremendous work” that those people do.

On the same program, he defended a statement he made last fall in which he said he “almost threw up” when he read former President John F. Kennedy’s famous speech to Baptist ministers in Houston during the 1960 presidential campaign. “To say that people of faith have no role in the public square?” he said. “You bet that makes you throw up.”

With former House speaker Newt Gingrich (Ga.) and Rep. Ron Paul (Tex.) also vowing to keep their campaigns going and the Republican electorate unwilling to coalesce around Romney, Republican governors see a distant possibility that the battle could continue to the national convention in August. But they dismissed talk of another candidate getting into the race.

Daniels and New Jersey Gov. Chris Christie, often cited as possible late entrants, said Sunday that they have no interest in the role.

Christie, appearing on CBS’s “Face the Nation,” twice said he does not want to enter the contest. “I’m with Governor Romney,” he said. “And one of the things people know about me is that when I make up my mind, it pretty much stays made.”

Daniels reiterated his long-standing position that he will not run. “I haven’t played any games with anybody,” he said in an interview. “Nothing has changed.”

Still, he acknowledged that the nomination battle has kept the possibility of a late entrant alive.

“The fact that no one has sewn it up like previous cycles means it’s a relevant question,” said Daniels, who is neutral about the race. “It wouldn’t have been a relevant question in previous cycles. This one’s different in so many ways.”

Most governors have not picked sides in the contest, but Romney has the biggest number among those who have. The latest endorsement came Sunday from Arizona Gov. Jan Brewer, who said she sees the him as the party’s most electable candidate

“I think Mitt is by far the person who can go in and win,” she said.

Michigan Gov. Rick Synder endorsed Romney almost two weeks ago and is predicting victory on Tuesday. He said Romney’s background in private business and as chief executive of Massachusetts are strong credentials. But he parted company with the former governor on the auto industry bailout — Romney opposed the bailout; Snyder said it worked. Snyder also disagrees with the negative campaign tactics that Romney and his rivals have adopted.

He said Romney would be better to stop explaining his opposition to the bailout and look to the future. And as a politician who tries to remain relentlessly positive, Snyder said, he wished all the Republicans would cease the attacks.

“I’m not a negative advertising kind of guy,” he said in an interview, adding: “I don’t make judgments about that, but I have my own philosophy that I believe is a better answer.”

Other governors expressed concerns that the nomination battle has created distractions from what they think should be the main message of the campaign — the economy and the nation’s debt and deficit problems.

Oklahoma Gov. Mary Fallin said in an interview that one challenge for the presidential candidates will be to keep the focus on those bread-and-butter issues.

“It has become a heated race, as we’ve seen,” she said, with the result that the candidates are “getting sidetracked on issues other than job creation and the national debt.”

She said the candidates are not solely responsible for that, because the debates have forced them to answer questions about many other issues. She said of the debates: “I don’t think it’s been helpful to the candidates on the Republican side. They’ve gotten off course. It’s not that they want to; it’s that when you get asked certain questions, you have to answer those questions.”

Governors interviewed said the fall campaign will be competitive, although in a state such as Michigan, the president has opened up a big lead in the polls. Snyder attributed that to improvements in the economy. Daniels said that when the race refocuses on the president’s record, the Republican nominee will have a strong case to make.

One risk is that the nomination battle will leave the eventual nominee weakened, rather than strengthened. Asked whether he thinks that could be happening to Romney, Walker said it is too soon to tell. But he said Romney needs a sharper message.

“As much as you want to be profound and in depth, you’ve got to be simple,” he said. “It’s got to be boiled down to a few direct points. It’s got to have a profound basis and substance to back it up, but it’s got to be more simply stated than it has in the past.”

Staff writer Philip Rucker contributed to this report.