Or, alternatively, I suspect that the Republicans will get one more thrashing during the 2010 midterms over their resistance to the stimulus package and will re-shape themselves as the modern-day inheritors of William Jennings Bryan, running to the left of the Democrats economically but retaining their zombie-like affection for the social stratification of the 19th century.
This, I'm almost certain now, is what will eventually happen. It's funny that many of the responses here say things like "emphasize free market economics" and "appeal more to minorities" when in reality these two strategies almost directly contradict each other. The Republican's hardline insistence on an unregulated economy is the main factor that doomed them among minorities in 2008, and I highly doubt these groups are going to be more receptive to it in 4-8 years time. Considering how a lot of Hispanics tend to be somewhat socially conservative or at least moderate and judging by the Black vote on Prop 8, it's clear that it was
not the Republicans' social views that made them unpalatable to most visible minorities.
I suppose it's possible that if a much larger proportion of Hispanics or Blacks enter the upper middle class, then free-market principles could be used to effectively appeal to them, but such a fundamental demographic shift is probably at least a generation away given the current state of the economy and the gradual nature of economic change. Although (like many moderates) I personally would love to see a libertarian-leaning Republican party, in the short-to-medium such a strategy is just not electorally feasible. Barring some massive improvement in the economy, their only chance is probably to become the more economically liberal party to lure in minorities/working-class Democrats while retaining their social conservatism (which actually doesn't alienate too large a swathe of the aforementioned groups). The downside of course is that you probably lose a lot of moderate/libertarian Republicans to the Democrats, but these groups really aren't that electorally significant in the current climate and should be easily outweighed by the other potential gains made with certain minorities/working-class whites.