For four years, the leader most capable of unifying the fractious Republican Party has been Barack Obama.
Now the Republicans find their divisions newly revealed in the raw. By exposing the party's vulnerability to potent demographic shifts, the 2012 results have set the stage for a struggle between those determined to re-brand the Republicans in a softer light and those yearning instead for ideological purity.
But before acceptance comes denial. And the party's first challenge, it seems in the immediate aftermath, is to find common ground simply in diagnosing the problem. While some leaders argued that basic mathematics dictates that the party must find new ways to talk about issues like immigration, abortion and same-sex marriage, others attributed Republican losses to poor candidate choice, messaging missteps and President Obama's superior political operation.
"We continually crank out moderate loser after moderate loser," said Joshua S. Treviño, a speechwriter in George W. Bush's administration who now works for the Texas Public Policy Foundation, a conservative group. He said Mitt Romney was part of a "pattern" of Republican nominees, preceded by John McCain, Bob Dole and George H.W. Bush, who were rejected by voters because of "perceived inauthenticity."
By contrast, Ralph Reed, the longtime Republican strategist and chairman of the Faith and Freedom Coalition, said he would redouble efforts over the next four years to recruit women, Latinos and young people as grass-roots organizers.
"I certainly get the fact that your daddy's Republican Party cannot win relying singularly on white voters and evangelicals alone -- as critical as I believe those voters are to a majority coalition," Mr. Reed said. "The good news for conservatives is there are many of those who have not always felt welcome in our ranks who share our values."
The re-election of Mr. Obama, despite the flagging economy and ambivalence about his leadership, left questions that Republicans may sort out only over time, starting with the direction set by the party's majority in the House and the run-up to the 2016 campaign.
Can the Republicans shore up their weaknesses purely with tonal changes on issues like abortion, immigration and same-sex marriage, along with a repackaging of conservative fiscal policy? Will it require real moderation on social and economic positions that the Tea Party movement and the conservative base consider inviolate?
Or is an embrace of unyielding conservatism required to rally an electorate that has grown cynical about candidates who shape-shift after the primaries?
The debate is already roiling, with early markers laid in postelection news conferences and the Sunday talk shows. On CNN's "State of the Union," Carlos Gutierrez, a commerce secretary under George W. Bush and a Romney adviser, blamed the loss "squarely on the far right wing of the Republican Party."
Countered Gary L. Bauer, the socially conservative former presidential candidate, "America is not demanding a second liberal party."
The Republican National Committee is undertaking a two-month series of polls, focus groups and outreach meetings about its message and mechanics, with added focus on Latino subgroups like Cubans, Mexicans and Puerto Ricans. Introspection will also be on the agenda when the Republican Governors Association convenes on Wednesday for a three-day meeting in Las Vegas.
"The question really is how do we set the best tone in delivering our conservative message so that it becomes attractive to more people," said Gov. Bob McDonnell of Virginia, the association's chairman. "Looking at how young voters and minority voters are voting, it's an unsustainable trajectory."
In addition to losing both the popular and electoral votes for president, the Republicans lost nearly every swing state. Although the race was far closer than in 2008, Mr. Romney won two million fewer votes than Mr. McCain did against Mr. Obama that year.
Democrats, once fearful of losing the Senate, gained one seat there and four in the House. They also added seats in state legislatures.
The Republicans' only bright spot, other than maintaining the House majority, came in governors' races. They picked up a long-elusive seat in North Carolina, bringing their total to 30, the most by either party in 12 years.
The longer-term concerns for Republicans were revealed in exit polling. While Mr. Romney won the votes of 59 percent of whites, 52 percent of men and 78 percent of white evangelicals, Mr. Obama claimed 55 percent of women, 60 percent of voters under 30, 93 percent of African-Americans and more than 70 percent of Latinos and Asians.
Although the president's majority shrunk nationally, he won a larger proportion of Latino and Asian votes than in 2008. Among Latinos, Mr. Romney did 17 percentage points worse than George W. Bush only eight years earlier.
Perhaps most ominous, the Latino share of the total vote rose to 10 percent from 8 percent in 2004, and the Asian share rose to 3 percent from 2 percent. The electorate is now 28 percent nonwhite, more than double the figure from two decades ago. That growth is certain to continue; in 2011, births to nonwhites outnumbered births to whites for the first time.
"It's stunning that Republicans won the white vote by 20 points and still lost," said Alan I. Abramowitz, a political scientist at Emory University who writes about polarization. Unless Republicans reverse the trend, he said, the rising strength of Latinos could doom their ability to map a winning electoral strategy. Colorado and Nevada could soon join California and New Mexico as noncompetitive states for Republicans in presidential elections, with Florida not far behind.
"And eventually Texas," Dr. Abramowitz added. "Not 4 years or 8 years from now, but in 12 or 16 years Texas is going to become a swing state. And if Texas becomes a swing state, it's all over."
Whit Ayres, a Republican pollster, noted that Mr. Romney did better than Mr. McCain among white voters, and won independents by 5 percentage points, all to no avail.
"It is patently obvious that unless Republicans do better among nonwhite voters, they will cease to be a viable national political party," Mr. Ayres said. "Obviously, doing something on immigration-related issues, like the Dream Act, is a start. But we're also going to have to address the fact that younger people tend to be less conservative on a number of hot-button social issues."
The imperative to reach Latinos may put pressure on Congressional Republicans to compromise with Mr. Obama on a bill that provides illegal immigrants, or at least those who arrived in the United States as children, with a path to legitimacy. Senate leaders in both parties announced on Sunday that they were renewing negotiations to seek a deal.
But the Republicans also will have to overcome the tone set by Republican-led states that have enacted tough new measures aimed at catching illegal immigrants. Latinos will never vote Republican, said Mr. Treviño, the former Bush speechwriter, "if they think your political party just doesn't want you as a neighbor."
Republican officials said that meant aggressively recruiting Hispanic candidates like Senator Marco Rubio of Florida and Senator-elect Ted Cruz of Texas, both sons of Cuban immigrants. And they said it required stressing common values, like opportunity, social conservatism and support for small business.
"The conservative movement should have particular appeal to people in minority and immigrant communities who are trying to make it," Mr. Rubio said after the election, "and Republicans need to work harder than ever to communicate our beliefs to them."
Mr. Rubio will be a featured speaker on Saturday at a fund-raiser in Iowa being hosted by Terry E. Branstad, the state's Republican governor.
Ryan R. Call, the state Republican chairman in Colorado, where Hispanics made up 14 percent of those who voted there last week, said the party had to find a way to stand firm on conservative principles while finding a "proactive response" on issues like immigration and gay rights.
"We can't simply be the party of no," he said.
But the party's staunchest conservatives, including leaders of the Tea Party movement, are not ready to yield. Many, including House incumbents from safe districts and deep-pocketed financiers, hold outsize influence in the party.
The conservative strategist Richard A. Viguerie kicked off a news conference in Washington on Wednesday by declaring that "the battle to take over the Republican Party begins today." He added, "Never again are we going to nominate a big-government, establishment Republican for president."
Mike Huckabee, a former Republican presidential candidate and current Fox News host, said in an interview that shifts in the party's approach to social issues would be difficult "because those are not political issues, they're deeply held moral positions by the people who hold them."
Similarly, Senator Patrick J. Toomey of Pennsylvania, a fiercely anti-tax Republican, said in an interview that the election results gave him little incentive to compromise on fiscal principles, including in the coming negotiations with Democrats over deficit reduction.
"We've been offering solutions, and the people who voted for those solutions were re-elected," Mr. Toomey said.
This article originally appeared in The New York Times.