Washington (CNN) -- Was it the wrong candidate, low voter turnout, a few dumb comments, a superstorm or falling out of touch with a shifting American demographic?
Listening to Republicans try to explain what went wrong in their worse-than-expected election thumping reveals a party struggling to define itself amid continuing change in the nation it seeks to lead.
"We have to allow for a period when it's going to be messy and in which there's going to be an attempt for the Republican Party to find its soul," noted Isabel Sawhill, a senior fellow in economic studies at the Brookings Institution. "It's a divided party, it seems to me right now."
The well-known division pits a loud and powerful conservative base, fueled in the past three years by the tea party movement, against a once-prevalent moderate faction now relegated to wing status.
Evidence of the competing camps includes several U.S. Senate races in which little-known tea party-backed candidates toppled veteran moderates in Republican primary races, then lost to Democrats in the general election.
That dynamic in 2010 and this year -- which brought political punch lines such as Christine O'Donnell and Richard Mourdock to the national debate -- cost Republicans any chance of toppling Democrats from their Senate majority.
Tuesday's election revealed a broader challenge for GOP leaders and strategists. The white vote that is the party's traditional electoral foundation dropped to 72% of the turnout -- its lowest level ever -- while the Latino vote that tilts strongly toward Democrats rose to double digits for the first time at 10%, according to exit polls.
Even more problematic for Republicans was that President Barack Obama won 55% of the women's vote, which comprised 53% of the overall count, the exit polls indicated, while GOP challenger Mitt Romney won 52% of the male vote.
That meant an advantage for Obama of more than 7 million in the women's vote, and more than 5.5 million when comparing the president's share of the women's vote with Romney's share of the men's vote. Overall, Obama beat Romney by just over 2 million votes.
To win the Republican primary, Romney had to adopt conservative stances on sensitive social issues -- such as opposing gay marriage, abortion and a pathway to legal status for many young undocumented immigrants -- which alienated increasingly significant demographics of the American electorate, analysts noted.
The former governor of moderate Massachusetts tried to move back to the political center in the final month of the campaign, but questions persisted about Republican stances on social issues.
"Latinos were disillusioned with Barack Obama, but they are absolutely terrified by the idea of Mitt Romney," GOP fundraiser Ana Navarro told CNN.
GOP strategist Lenny McAllister said Thursday that the problem involved both substance and style.
"I think that when it comes to our principles, when it comes to the economy, when it comes to education and some of the things that we want to offer the American people, the Republican Party and our conservative principles have something to offer Latinos and African-Americans," McAllister told CNN.
"But when you're talking about electrified fences and you're talking about voter suppression, you're not going to win any voters within those two groups," he continued. "And that's the reason why we need leaders within the conservative movement and the Republican Party that can articulate the values without going down that very dangerous and insulting path that we saw throughout 2012."
House Speaker John Boehner, the de facto leader of the party in the election's aftermath, acknowledged Friday that a necessary internal discussion had started.
"It's clear that as a political party we've got some work to do," Boehner told reporters, adding that "the principles of our party are sound" but the question is "how we talk about who we are as a party."
For now, "conversations are under way and will continue," Boehner said.
That message seemed lost on many conservatives, at least in their initial reactions.
Some blamed the Romney loss on Superstorm Sandy, which slammed the East Coast from Maryland to Connecticut to disrupt campaigning the week before the election. Former Mississippi Gov. Haley Barbour told CNN the storm and its aftermath halted Romney's momentum.
At a news conference Wednesday, a coalition of social conservatives and tea party activists said Romney's campaign failed to represent them on a national level.
"Conservatives were left out in the cold," complained Brent Bozell, president of the conservative Media Research Center. "It should have been a landslide for Romney, had he embraced a truly conservative agenda."
In a campaign defined by bitter attacks on both sides, Bozell faulted Romney for not being even more aggressive, saying, "It should have been a cakewalk for Romney to define (the president), but he didn't -- hence Obama's victory."
Meanwhile, Marjorie Dannenfelser of the anti-abortion rights group Susan B. Anthony List criticized Romney for failing to make abortion a central campaign issue. Stronger attacks on the administration's policies, such as a requirement that religious organizations provide their employees with health care coverage that she said included abortion-inducing drugs, would have attracted more support from uncommitted voters, Dannenfelser argued.
"He took all the right stances," she said. "The problem was not communicating on the national stage with Obama what (the president's) actual positions were."
Her group endorsed Romney, Dannenfelser said, adding, "We assumed that given who he was, he would make (abortion) more of a national issue."
According to exit polls, 59% of voters think abortion should be legal in the United States, compared with 36% who said it should be illegal.
Jenny Beth Martin, co-founder of Tea Party Patriots, pinned the election loss on "a weak, moderate candidate, hand-picked by the Beltway elites and country club establishment wing of the Republican Party."
Her claim elicited a vulgarity from retiring Rep. Steve LaTourette, a moderate Republican who told CNN on Thursday: "There's a one-word phrase we use in Ohio for that: crap."
LaTourette says the hyper-partisan environment in Washington politics prompted him not to run for a 10th term this year. He attributed his party's election failure on far-right viewpoints on social issues, saying the GOP needs to "get out of peoples' lives, get out of their bedrooms."
"We sent (women) running back to the Democratic Party because they think we're nutty," LaTourette said of comments about rape by Mourdock of Indiana and Rep. Todd Akin of Missouri, conservatives who both lost Senate races Tuesday in states won by Romney.
Mourdock came under criticism for saying it was God's will when a child is conceived by rape, while Akin was forced to apologize and declare as wrong his statement that "legitimate" rape rarely causes pregnancy.
Another retiring Republican, Sen. Kay Bailey Hutchison of Texas, also cited the comments by Mourdock and Akin as detrimental.
"We had Republican candidates who got very high profile and said some very stupid things. I think that really tainted the party," Hutchison told CNN on Thursday, adding: "People have personal beliefs, and what we need to do is fashion a party around the economics and the long-term viability of the economy of our country. When people start trying to go into such personal issues and then try to form a party around it, it's very difficult."
To McAllister, the GOP strategist, it comes down to Republicans needing to get better at communicating their core principles.
"They haven't been able to articulate the conservative Republican message without being insulting," he said. "I think that, moving forward, you'll see some leaders be able to do that extremely well. And you'll continue to see others that slip when it comes to this."
Other Republicans said the party needs to broaden its base by becoming more inclusive to minorities.
"The question is do they want to, in a disciplined way, create a schedule and a program and include people who are not traditionally Republican," said former House Speaker Newt Gingrich, who lost to Romney in the GOP primary race this year.
Hutchison called Texas a possible model for the party, noting it permits some children of illegal immigrants to attend state universities and that her successor in the Senate will be Ted Cruz, whose family came from Cuba.
"I think Texas is a way forward to show you can be very conservative and talk about the issues that Hispanics ... embrace," she said.
While losing the presidential race and failing to win a Senate majority, Republicans held on to their control of the U.S. House, setting up a repeat of the political breakdown in Washington of the past two years.
Some Republicans say the gridlock of the 112th Congress, which concludes at the end of the year, may give way to a new sense of cooperation in the session that starts in January, motivated by a political survival instinct if nothing else.
"I think, finally, everybody will start working together, because over the last three terms, we've seen everybody be humiliated and be humbled a little bit," McAllister said. "In 2008, it was the Republicans. In 2010, it was the Democrats. In 2012, it's been the tea party element. So, everybody has finally been humbled to a point where they have to come to the table and start working for Americans, not just for their own political interest."
Sawhill, the Brookings fellow, said she expected moderate elements of traditional Republican support -- such as the business community -- to pressure party leaders to work with Democrats on solutions to vexing problems such as a comprehensive agreement to reduce federal deficits and debts. Citing the "public disenchantment with the way Washington is working, she told a post-election forum Wednesday that Republicans "have to work a little harder to make sure there is more compromise in the future."
The initials signs were mixed. Boehner expressed a desire to work out a deal with Obama and Democrats during the week and at a news conference on Friday.
However, he stuck to the hard-line Republican position of no tax increases as part of a package including spending cuts and entitlement reforms.
"Raising tax rates will slow down our ability to create the jobs everyone says they want," Boehner said Friday, noting that higher taxes on the wealthy will hit small business owners. But he also said that "everything on the revenue side and on the spending side has to be looked at."
Earlier this week, Senate Republican Leader Mitch McConnell of Kentucky said the Democratic plan to let tax cuts from President George W. Bush's administration expire for income over $250,000 would be rejected by congressional Republicans.
"Now is the time for the president to propose solutions that actually have a chance of passing the Republican-controlled House and a closely divided Senate," McConnell said in a prepared statement.
His Democratic counterpart in the Senate, Majority Leader Harry Reid of Nevada, said the election results show the public backs the Democratic position that was a staple of Obama's campaign.
"There was a message sent to us by the American people, based on the campaign," Reid said at a news conference Wednesday. "People making all this money have to contribute a little bit more."
CNN's Ashley Killough, Peter Hamby, Ted Barrett and Deirdre Walsh contributed to this report.