Republican leaders awoke Wednesday to witness their grim future. And then they promptly began what promises to be an extended period of internal strife over how a party that skews toward older white men can compete in an increasingly diverse nation.

President Obama’s decisive victory over Mitt Romney served as a clinic in 21st-century politics, reflecting expanded power for black and Hispanic voters, persistent strength among women, a dominant showing among young voters, and even a rise in support among Asians.

Nationally, the steady and inexorable decline of the white share of the electorate continued, dropping to 72 percent, down from 74 percent in 2008 and 77 percent in 2004, according to exit polls.

The Hispanic share ticked higher again, for the first time encompassing one in 10 voters nationally and reaching especially high levels again in states such as Colorado, Nevada and New Mexico, which have become comfortable turf for Democrats.

The breadth of the Democratic dominance was shown across the battlegrounds, where Obama drew the support of different groups to win in different places.

In Colorado, he captured three-quarters of Hispanic voters, up from 61 percent in 2008. He also improved his Hispanic performance in Florida, a result that included dominance of the heavily Puerto Rican swing precincts around Orlando and the election of a Cuban American Democrat to Congress, symbolizing the end of the GOP’s decades-long lock on that community.

In Ohio, African Americans showed up in large numbers and offered near-unanimous support to reelect the country’s first black president. Black in that state accounted for 15 percent of the electorate, up from 11 percent four years ago.

In Iowa and New Hampshire, states without big minority populations, Obama won by gaining the support of nearly six in 10 women.

The Republicans’ troubles were further illustrated by a string of victories for gays, including voter approval of same-sex marriage in Maine, Maryland and Washington state, and the election of the country’s first openly gay U.S. senator, Tammy Baldwin of Wisconsin, a state many Republicans thought would go their way.

“We’re going the way of the dinosaurs, and quick,” said David Johnson, a top GOP strategist in Florida. “The meteor’s already hit, and we’re just trying to wonder what the blast zone will look like.”

The challenge for Democrats moving forward will be re-creating the Obama coalition in the post-Obama era, when candidates may lack the charisma or personal connection to the party’s core African American constituency. And just as Obama emerged to reorder the nation’s politics, so, too, could a transformational figure emerge on the right.

Still, that Tuesday’s results assured victory for a president facing a still-fragile economy, a high unemployment rate and a record of enacting divisive legislation confounded many Republicans, who had hoped that Obama’s 2008 strength would reflect an anomaly and not a trend.

Concerns Wednesday ranged beyond the party’s glaring demographic challenges. Some strategists pointed to a string of Senate defeats in the GOP-friendly states of Indiana, Missouri, Montana and North Dakota as evidence of poor candidate recruitment by party leaders.

In the immediate aftermath of Republican losses, there was little consensus on how to regroup. Many argued for a deeper embrace of core conservative principles, while many others said that catering to the conservative tea party base was the problem. Some wanted a greater emphasis on social issues, while others said social issues should be dropped.

Illustrating the divide, Carl Forti, a longtime GOP strategist, said he worried that some in his party would “take the wrong message away from this and think we need to be more conservative and more tea-partyish.” Party activist Richard Viguerie toed the opposite line, declaring: “Far from signaling a rejection of the tea party or grass-roots conservatives, the disaster of 2012 signals the beginning of the battle to take over the Republican Party and the opportunity to establish the GOP as the party of small-government constitutional conservatism.”

Democrats on Wednesday were assessing a far brighter reality. Although the results showed declines in support among white and Jewish voters and weakness among union voters, party strategists noted that the share of the electorate younger than 30 grew again, enhancing what they consider a generational shift in their direction. If Republicans seemed to cling to a 20th-century formula that helped elect Ronald Reagan — 89 percent of Romney’s voters nationally were white — Democrats saw in Tuesday’s results the contours of their long-lasting coalition.

“This election affirms that there is a new politics, a new demographic reality in America, and that the Democrats are further along in adapting their politics to these new realities than the Republicans are,” said Simon Rosenberg, whose liberal NDN think tank has been tracking the changing Hispanic electorate and other trends.

Obama’s success followed intense efforts by his campaign and outside groups to recruit and register minority voters. The campaign registered hundreds of thousands of blacks and Hispanics in Florida alone, surpassing its 2008 efforts. Nationally, the NAACP aimed to bring 1 million new African Americans into the electorate, and the Service Employees International Union devoted much of its $75 million effort to registering minorities in eight battleground states.

The challenges are deep for Republicans hoping to address the issues, illustrated most clearly by the fate of Romney’s campaign. Once viewed as a centrist with potentially broad appeal, the former Massachusetts governor was compelled over two presidential campaigns to shift far to the right, particularly on immigration, in a way that alienated many Hispanic and centrist voters.

Republican rhetoric, many party strategists say, has made immigration more of an identity issue, turning off even those Hispanic voters who might agree with the GOP on many subjects.

Javier Ortiz, a Republican strategist who advises his party’s congressional leadership, said early Wednesday that he had been in touch with senior officials about formulating a new approach to minority outreach. Such conversations have been happening for a few years, he said, but Tuesday’s election results should move them along more briskly.

“If these results do not escalate the conversation, then we’re doomed,” Ortiz said.

Former Mississippi governor Haley Barbour predicted that, within four years, the GOP would forge a new pro-immigration policy, mostly because the country’s economy depends on migrant workers. “Then the politics will take care of itself,” he said. “I don’t think the Democrats are being realistic if they think this is some permanent condition among Latinos.”

Some conservative leaders called for a purge of sorts to rid the party of stodgy, old-school voices.

Al Cardenas, the Cuban American chairman of the American Conservative Union, said GOP officials must ask longtime county and local party chairmen to resign to make way for more diversity. “It’s very hard, but this has gotten to a crisis point,” he said.

One place that conversation will happen is the weekly meeting of conservative movement leaders, headed by anti-tax activist Grover Norquist. Norquist said the party faces a difficult task of minimizing the power of immigration hard-liners.

“Ten years from now, you want to be splitting the Hispanic vote by something close to 50-50,” he said. “That’s completely doable if the threat of deportation was removed. But it’s not doable as long as that’s hanging over, and some Republicans talk as if they’re for the deportation of your mother or your aunt.”

Big questions loomed Wednesday about who, in a party without a clear national leader, would push the GOP to transform itself.

House Speaker John A. Boehner (Ohio) faces a daunting task of holding together his coalition, which is dominated by tea party conservatives skeptical of liberal immigration laws.

Evangelicals remained a strong piece of the GOP coalition, voting more solidly for Romney — a member of the Church of Jesus Christ of Latter-day Saints — than they did four years ago for Sen. John McCain (Ariz.). That makes it unlikely that the party will relent on its staunch opposition to same-sex marriage.

“The Republican coalition is the same coalition as it’s been for years: culturally conservative, small government, lower taxes, pro-family, pro-life and strong national defense,” said Gary Bauer, president of American Values, an evangelical group. “I don’t know of anything in that agenda that we would want to drop.”

Scott Clement contributed to this report.