Shaping the next phase in the history of the Republican party is an ongoing project that won't really be completed until they have another president, and their 2016 nominee could well be that person. Part of what makes this process interesting is that there is no obvious choice. Republicans are famous for nominating the person who is "next in line," usually someone who ran previously and lost. Every Republican nominee dating back to Richard Nixon has fit this pattern, with the exception of George W. Bush in 2000 (and Gerald Ford, who is obviously a special case). But the people who lost to Mitt Romney in 2012 revealed themselves to be an extraordinarily unappealing group; Paul Ryan didn't exactly emerge from the race looking like a giant; and there are multiple governors like Bobby Jindal and Mitch Daniels who could be strong competitors. So the next GOP nominee could be a hard-right conservative, or a relative moderate, or something in between.
As E.J. Dionne points out in his column today, when a party spend some time in the wilderness, its path back to power usually involves some ideological accommodation:
After losing throughout the 1930s and ’40s, Republicans finally came to terms with the New Deal and elected Dwight Eisenhower in 1952. Democrats lost three elections in the 1980s and did a lot of rethinking inspired by Bill Clinton, who won the White House in 1992. In Britain, the Labor Party learned a great deal during its exile from power in the Margaret Thatcher years. The same thing happened to the Conservatives during Tony Blair’s long run.
Coming to terms with your opponents' successes doesn't necessarily mean accepting them in your heart; it can mean merely that you'll put off trying to undo them. This is what Republicans have done with the New Deal, and then with Medicare and the rest of Lyndon Johnson's Great Society programs. Republicans would love to repeal Medicare entirely (it is, after all, a single-payer government health care scheme), but failing that they'd still like to privatize it. Efforts to that end have so far been unsuccessful, however, and they feel the political need to pose as the program's defenders. But that's still a significant accommodation, one that helps the program survive.
So what are the chances the next Republican nominee will actually characterize his or her own candidacy as a move to the center? It may be almost impossible to imagine from today's vantage point, but things can change quickly. Mitt Romney's formula was to be extremely conservative on substance, while hoping that eventually he'd find a way to appeal to the center, and it failed. This is the inverse of the formula that Dionne is talking about, the one that brought success to Bill Clinton, Tony Blair, and David Cameron. There are obviously plenty of differences between those three, but they all constructed a policy array more to the center than their party's predecessors, which broadened their electoral coalition, but found a way to bring along their base as well, even if it was only through personal charisma. You may not remember, but George W. Bush did something similar: he ran a campaign that looked extremely centrist, all about "compassionate conservatism," issues Republicans usually didn't stress (he ran innumerable TV ads about education), and getting beyond the partisanship of the past.
For all that the GOP has been purged of moderates, it's entirely possible that the right 2016 candidate could craft a centrist appeal for the broader electorate, and successfully say to the party's base, "You've been suffering under Barack Obama for eight long years. If you follow me, we'll reach the promised land." Remembering how liberals felt after eight years of Bush, I wouldn't be at all surprised if the base, or enough of them anyway, went along for the ride. One person can make all the difference, if it's the right person at the right time. And then the party would begin a move back from the ideological fringe, one that looks all but impossible today. Stranger things have happened.