I'm very much enjoying David Frum's e-booklet Why Romney Lost and thought this point (which doesn't really explain why Romney lost) is an underappreciated one:
For example: it’s certainly possible for Republicans to choose to be a white person’s party. If we do so choose, however, we are also choosing to be an old person’s party. Since the elderly receive by far the largest portion of government’s benefits, an old person’s party will be drawn by almost inescapable necessity to become a big government party. Indeed that is just what happened in the George W. Bush years: Medicare Part D and all that.
What's more, while it's not super-polite to say so it's important to understand that among the white population generally racist sentiments correlate with more support for programs for the elderly and less support for programs for the poor. Which is just to say that while from some kind of abstract political theory point of view you can judge "get the government out of my Medicare" sentiment to be incoherent, in terms of coalitions there's a deep logic here. Older people are whiter and more socially conservative than younger people. More ethnocentric white people of all ages are more supportive of programs for the elderly. So a coalitional core of older white social conservatives makes perfect sense.
An interesting problem here is that at the elite level conservative leaders simply don't like the idea of this coalition. Paul Ryan seemed most thrilling when he was most daring in his attacks on social insurance for the elderly. George W Bush masterfully led this coalition through the Medicare Part D episode only to attempt to spend his political capital on a phase-out of Social Security.
So I would say that a much bigger issue for the GOP than why they won or lost a particular election (at the end of the day, incumbent presidents normally win) is simply that the actual coalition the party has is ill-suited to the agenda the coalition's leaders seem to want to pursue. Elite conservatives are well-aware that it's retirement programs that account for the bulk of non-military spending. And I think that at a level of rhetoric and politicking, the Romey / Ryan / Boehner / McConnell GOP has done about a good a job as you could hope of squaring this particular circle. It's just hard. So one option would be to stay committed to the idea of dismantling the welfare state and try to ditch the existing coalition in favor of some different, younger, less-white, less-ethnocentric coalition that's more likely to want to cut retirement security programs. That would involve moderating on immigration and many social issues, but since (unlike gay rights) abortion is not an age-polarized issue the GOP could remain robustly anti-abortion. Then you might try to get to the Democrats "left" on certain topics where younger people tend to have small government views—marijuana regulation and copyright policy, for example—reversing the traditional logic of fusionist politics.
The alternative would be to take the existing Republican Party base as a given and simply abandon the quest to dismantle the welfare state. One argument for that approach is there's some reason to think that dismantling the welfare state is impossible anyway. Obviously, that kind of agenda wouldn't support Reagan-style robust tax cutting. But it could still push to make the tax code flatter—i.e., less of a mechanism of redistribution—which was in fact one version of the Schrodinger's Tax Plan that the party put forth in 2012.