Boehner and Senate GOP Leader Mitch McConnell will stand at the center of the intra-party debate. Within days they must decide how to negotiate with Obama and Democratic lawmakers on the looming "fiscal cliff," a package of major tax hikes and spending cuts scheduled for the new year.
McConnell issued a defiant statement Wednesday. "The voters have not endorsed the failures or excesses of the president's first term," he said. "They have simply given him more time to finish the job they asked him to do together with a Congress that restored balance to Washington."
Boehner was more conciliatory in tone when he addressed reporters Wednesday. But he recommended Romney's tax package — including rate cuts for everyone and the elimination of yet-to-be-named deductions — which he said would create a net increase in government revenue.
Obama has insisted that the wealthiest Americans pay higher tax rates, as they did under Clinton. Many Democrats in Congress agree.
Republican insiders, meanwhile, nervously focused on an approaching problem that could produce even bigger presidential losses in future years. The GOP relies overwhelmingly on white voters, a steadily shrinking share of the population. Hispanics, the nation's fastest-growing group, have bristled at Republican attacks on illegal immigration, which some people consider a slap at all Latinos, legal or not.
Republican campaign pros said the party must find a way to temper the talk about immigration without infuriating conservatives who oppose "amnesty" for those who entered the country illegally.
"You can't just say 'If you fix the tone, you fix the problem,'" said Republican consultant Terry Nelson. "We have to figure out what kind of policy solutions we have for this."
Ullyot said congressional Republicans should embrace more lenient immigration policies immediately.
On still another front, many Republicans said their party must find ways to appeal to women, who voted heavily for Obama. The party cannot give people the impression that opposing abortion is its top women-related issue, said Rep. Ileana Ros-Lehtinen, R-Fla.
"Single moms are part of our American fabric," she said. "Let's not keep thinking that the American family is made up of a mom and a dad and two kids and a picket fence and a dog and a cat. It's made up of a lot of single moms struggling to make ends meet. ... We need to get a program to say 'we care about you.'"
Associated Press writers Ken Thomas, Suzette Laboy and Director of Polling Jennifer Agiesta contributed to this report.