And Mark McKinnon, another former strategist for President Bush and Mr. McCain, argued that the party “needs messages and policies that appeal to a broader audience.”

“This election proved that trying to expand a shrinking base ain’t gonna cut it,” Mr. McKinnon said in an e-mail. “It’s time to put some compassion back in conservatism. The party needs more tolerance, more diversity and a deeper appreciation for the concerns of the middle class.”

But not everyone was urging the party to run to the center. “No doubt the media will insist that Republicans must change, must sprint to the center, must embrace social liberalism, must accept that America is destined to play a less dominant role in the world,” Fred Barnes wrote on the blog of The Weekly Standard. “All that is hogwash, which is why Republicans are likely to reject it. Their ideology is not a problem.”

“But there is also a hole in the Republican electorate,” he continued. “There aren’t enough Hispanics. As long as two-thirds of the growing Hispanic voting bloc lines up with Democrats, it will be increasingly difficult (though hardly impossible) for Republicans to win national elections. When George W. Bush won a narrow re-election in 2004, he got 44 percent of the Hispanic vote. If Romney had managed that, he would have come closer to winning. He might even have won.”

And Erick Erickson made this plea at RedState.com: “Just please, G.O.P., please — in four years let’s not go with the ‘he’s the most electable’ argument. The most electable usually aren’t.”

Richard A. Viguerie, the chairman of ConservativeHQ.com and a pioneer in the field of political direct mail, released a statement saying that the party should never again nominate “a biggovernment establishment Republican” for president.

“Mitt Romney’s loss was the death rattle of the establishment G.O.P.,” Mr. Viguerie said in the statement. “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 G.O.P. as the party of small-government constitutional conservatism.”