I don't see the Republican party lasting too much longer in its current form (super-religious, super white, etc.).
Therefore, I think the two party system will have to split along different lines (i.e. gay marriage will be legalized and become a non-issue... other social issues will move in that direction too)...
Republican Party = Libertarian, fiscally conservative, socially libertarian live and let live.
Democratic Party = Fiscally liberal, not socialist but moving in that direction, socially still more liberal and using the government to solve social problems.
I could actually see Republicans becoming competitive in states like New Hampshire, Maine, Connecticut, Oregon, Pennsylvania, Wisconsin, Minnesota, Michigan, Iowa again... and Democrats becoming competitive in Texas, Georgia, Arizona, etc.
And what happens to the social conservatives? Do they form their own party? Or do you intend to purge them?
The suggestion that the Republicans are suddenly going to be what liberals want them to be is mind-boggling. If anything, the Republican Party will become even less attractive to Internet liberals, as it's probably going down the road to become a sort of Third Positionist political outfit. As it declines in numbers, the GOP will become more, not less, extreme in its rhetoric and policy positioning. As more and more Hispanic immigrants make it to the polls and the country becomes majority-minority, the Republican Party will be more of a 'white man's party' than the vast majority of liberals can scarcely imagine. I'm talking about a party that will openly advocate closing the borders outright. This of course will likely alienate the business community from the GOP, which will continue moving towards the Democratic Party.
The Democratic Party on the other hand will morph into a weird kind of 'market social democracy' party which enacts social democratic ends by market means. Thus it'll kind of be a crony capitalist party with a lot of big friends on Wall Street that it funnels state funds as the state itself becomes a sort of middleman between corporate America and literally everyone else. We'll have universal healthcare, higher education, all that, but it'll be thoroughly corporatized; that is, we'll have them on the terms of the massive international corporations that control our politics, not on the terms of a democratic citizenry. Imagine Obamacare, but replicated on a massive scale. It won't be a traditional 20th century welfare state (because organized labor will be essentially neutralized), but rather a massive, bloated middleman state where tax dollars are shifted through various corporate organs to deliver the public a product, rather than a public service. There will still be a 'pity-charity' welfare state, but it'll be on the terms of the corporate elite that runs the country and the Democratic Party, not the public at-large. Food stamps* will still exist, as will traditional welfare, but these programs will be changed beyond recognition; Social Security will be privatized, turned into something that some parasitic Wall Street middleman can turn a profit off of, and Medicare will likewise be the same, turned into a functional extension of Obamacare by enterprising Democratic politicians.
*Food Stamps will very likely be limited in nature to promote 'healthy diets,' aka no more using food stamps to buy soda and potato chips, you must buy organic arugula or something.
The Democratic Party will be so fractious and heterogeneous that their coalition simply will not last (assuming, of course, that the party becomes such in the future). What you describe here is unthinkable; the most likely scenario is that Republicans will chip away at the minority vote over time and continue to remain viable.
My opinion on the future parties:
Republicans-Largely the same as today, but with a slightly broader tent. They will find a way to change their messaging to appeal to minorities.
Democrats-Largely the same as today, but more minority dominated. Liberals complain about disagreements within their own party; well, it is only likely to get worse as America gets more diverse (hey, that rhymes).
