According to exit polls, about 7 in 10 Hispanics said they were voting for Mr. Obama. Mr. Romney won the support of nearly 6 in 10 whites. In urban areas, white voters were split over the two candidates, but about 6 in 10 white voters in the suburbs went for Mr. Romney, as did nearly two-thirds in rural areas.

Mr. Romney won a majority of voters 65 or older, while Mr. Obama was backed by 6 in 10 Americans under 30, and won a narrow majority of those under 44.

Even as they absorbed Mr. Romney’s defeat, the party’s top elected officials, strategists and activists said they believed that Republicans had offered a persuasive message of economic opportunism and fiscal restraint. While the messenger may have been flawed, they argued, Republicans should not stray from that approach in a moment of panic.

“The party has to continually ask ourselves, what do we represent?” said Senator Marco Rubio, the Florida Republican seen as a top White House contender in 2016. “But we have to remain the movement on behalf of upward mobility, the party people identify with their hopes and dreams. People want to have a chance.”

Matt Kibbe, the president of the Tea Party-aligned group FreedomWorks, acknowledged there would be a natural struggle for the identity of the party in the election’s aftermath. But he argued that in some respects the fight had already been waged and won by the energized grass-roots forces that have shaped the contours of Republican politics in recent elections.

“You are going to see a continuation of the fight between the old guard and all of the new blood that has come in since 2010, but I don’t know how dramatic it is going to be,” he said. “It is getting to point where you can’t reach back and pull another establishment Republican from the queue like we have done with Romney.”

Besides Mr. Rubio, Representative Paul D. Ryan, the unsuccessful vice-presidential candidate, will now be seen as a chief party voice, as will Gov. Scott Walker of Wisconsin. House Republicans particularly can be expected to gravitate to Mr. Ryan. Among others considered on the rise are Senator Rand Paul of Kentucky, Gov. Bob McDonnell of Virginia and Gov. Bobby Jindal of Louisiana, and all can to some extent attribute their success to Tea Party-style politics with an emphasis on cutting spending and shrinking government.