WASHINGTON — Democratic governors are bullish on President Barack Obama’s re-election prospects, citing the improving economy and a Republican nominating contest that has exposed deep divisions in the party’s base.

Republican governors insist Obama is vulnerable, but they say they are concerned the prolonged primary race has alienated independent voters and may have badly damaged the eventual nominee.

Democratic enthusiasm and Republican apprehension were both on display at the winter meeting of the National Governors Association, an annual four-day conference where states’ top executives gather to discuss policy and trade ideas on best practices but where politics are always close to the surface.

Maine Republican Gov. Paul LePage suggested the drawn-out negativity of the contest could mean Republicans should reach for a new candidate strong enough to defeat the president.

“If they continue to beat each other up, then maybe we should get somebody unknown to go against Obama. They’re damaging themselves,” LePage said. “It’s like a marital battle. Somebody’s got to apologize.”

LePage said he was not impressed with the field of contenders.

The tea party favorite when he was elected in 2010 told Maine Today Media in Sunday’s editions that his party needs a “fresh face” to challenge Obama.

LePage said at the governors meeting that he was hoping for a floor fight at the party convention to choose a nominee.

“I would love to see a good old-fashioned convention and a dark horse come out and do it in the fall,” LePage said, adding that he didn’t have a particular alternative candidate in mind.

“The candidates in this primary have beat themselves up so badly it would be nice to have a fresh face that we all could say, ‘OK.’ The country deserves better than having people stand up and keep criticizing each other,” LePage said.

After LePage’s comments to reporters, his press secretary emailed a clarification to reporters saying that the governor would support whoever wins the nomination and that the country is better off electing anyone over Obama.

LePage also criticized the Maine Republican Party’s handling of its nonbinding presidential caucuses, saying they were “poorly handled.”

Romney was declared the winner of the caucuses earlier this month, but the exclusion of postponed caucuses in Washington County and the need for a recount because of a variety of counting mistakes and omissions drew widespread criticism.

Many Democratic governors seemed almost giddy about Obama’s chances of winning a second term.

They pointed to the improving employment figures, which have helped raise state revenues after years of painful budget cuts. The national unemployment rate stood at 8.3 percent in January, down from a high of 10 percent in October 2009.

“These Republicans that are running for president, they’re so depressing. Cheer up!” Vermont Gov. Peter Shumlin said after Democratic governors left a White House meeting with Obama. “We’ve got some good news: a great president creating jobs, and governors who are seeing revenues rebound.”

Even Democratic governors of some typically toss-up — or “purple” — states, said they like Obama’s chances.

“In a purple state people want to see results and they also want to see a level of collaboration and teamwork. I think he is going to win Colorado,” the state’s governor, John Hickenlooper, said.

Meanwhile, virtually no Republican governors were willing to predict their party’s nominee would prevail in November.

Many lamented the drawn-out nature of the nominating process, in which the early front-runner, former Massachusetts Gov. Mitt Romney, has been weakened by the intense scrutiny of his wealth, business practices and shifts on issues as well as the unwillingness of conservative voters to rally behind his candidacy. Many conservatives have coalesced recently around former Pennsylvania Sen. Rick Santorum, Romney’s latest strongest rival as the contest moves to primaries in Arizona and Michigan on Tuesday and 10 contests on March 6.

Indiana Republican Gov. Mitch Daniels chimed in on the Republicans’ disarray, saying, “I don’t know anybody who thinks if you started out to design a good process to pick a president you’d choose exactly what we have now. Daniels is a former White House budget director who explored a presidential candidacy but ultimately decided against a run.

Daniels said he would not consider jumping into the race even if Romney were to lose Michigan. Some Republican leaders have said privately that if Romney does not prevail in Michigan — a state where he was born and grew up and where his father served as governor — the defeat could serve as an opening for a party heavyweight like Daniels to join the field.

Daniels, who has not endorsed a candidate, said he didn’t believe a potential Romney loss in Michigan indicated unremitting problems with his candidacy.

“The problem I would worry about, and have all along, is that our side might not offer a bold enough and specific enough and constructive enough and, I would say, inclusive enough alternative to America,” Daniels said.

Tennessee Gov. Bill Haslam, who has endorsed Romney, refused to predict Romney would win Tennessee when voters go to the polls there on Super Tuesday. But he said he felt confident Romney was the strongest candidate to challenge Obama in the general election, in part because he could win unaffiliated voters.

“I think we’ll be in for a long election night regardless. I think the race will be close,” Haslam said. “That’s why it’s important for Republicans to do a great job expressing our case and reaching out to independents.”

Some Republican governors voiced concern that social issues like contraception and gay marriage had at times eclipsed discussion of the economy in the primary race.

“I do agree those social issues are not as significant as some of the economic and fiscal issues that really threaten our way of life,” South Dakota Gov. Dennis Daugaard said, saying he was worried the debate over such issues might alienate uncommitted voters.

Contraception emerged as a hot button issue last month after the Obama administration announced it would require church-affiliated employers to include birth control as part of an employee’s health insurance coverage. The decision drew outrage from Catholic bishops and other religious leaders, and Obama eventually retooled the requirement to say health insurers, not the religious groups themselves, must pay for the coverage.

Many Republicans, including the leading presidential candidates, slammed Obama for what they called government infringement on religious liberty. But their hard line risked making the candidates look as though they were anti-birth control — particularly Santorum, a devout Roman Catholic who has said he believes contraception is harmful to women.

The problem was further compounded when Virginia Gov. Bob McDonnell, a rising Republican star widely considered a contender for the vice presidential nomination, backed a controversial bill that would have required women undergo a vaginal ultrasound before receiving an abortion.

McDonnell backed down this week, asking the bill’s sponsors to require a less invasive ultrasound procedure instead. But the controversy drew national attention and scorn from women’s groups.

Pennsylvania Republican Gov. Tom Corbett said he wasn’t concerned that social issues had become part of the presidential campaign, saying such topics are top concerns for many Republican voters. But Corbett, who hasn’t endorsed a primary candidate, said the discussion would shift once a nominee is chosen.

“It will be the economy, the economy, the economy and it will be jobs, jobs, jobs. And I think that’s exactly where it should be,” Corbett said.