The question now facing Republicans is whether they shift toward the middle or instead try to appeal to growing demographic groups while staying planted firmly on the right side of the political spectrum. There are those who will look at the past two presidential cycles, in which relatively moderate Republican nominees fell short, and conclude that the party needs to nominate a true believer willing to stand behind core conservative principles. Rubio, who is already being discussed as a leading 2016 presidential contender, is the kind of candidate that could energize those who want to reach out to new types of voters without abandoning the party's beliefs.

John Hudak of the Brookings Institution argues that the best past forward for the GOP is to move - slowly - toward positions that hold appeal for groups that voted for Mr. Obama this year.

"If they move too quickly to the middle, it's going to alienate a lot of people in their party," he said. Fifty-nine percent of voters in the exit poll said abortion should be legal, but if Republicans suddenly embrace abortion rights, evangelicals and values voters could abandon the GOP. If they shift leftward too quickly on fiscal issues, it could prompt Tea Partiers and libertarians to do the same.

Hudak said the GOP's handling of same-sex marriage provides a template. In the 2004 election, Republicans used opposition to same-sex marriage to drive voters to the polls. But as attitudes shifted, Republicans for the most part simply stopped talking about the issue.

"That's the first step to neutralizing these social issues," he said. "It's not to change your mind. It's just to not speak your mind. And that way people can think this isn't that aggressive party anymore, and it opens the door for them to vote for you based on other issues."

"It's definitely a challenge," Hudak added, "but I don't think it's insurmountable."