Well, the upside is that as the republicans push further and further to the right (and drive more and more to the left), eventually their vote margin will drop to null, at which point two things could happen:
1) They go back left to recover
2) They stay right and become meaningless while the Democrats eventually split because there must always be more than one party
I think a political realignment of some sort is probably going to occur before long, though it might take a crisis to trigger it. Situation 1) is pretty much inevitable, though it might take a couple decades. No party's gone defunct since the Whigs, who collapsed 160 years ago, and that was after an ideological split so bitter that the incumbent president couldn't get his own party's renomination. (Mind you, that's not an impossibility- it seems entirely possible for Jeb Bush, say, to pass immigration reform with mostly Democratic votes in Congress, and face an intense primary challenge from Ted Cruz.)
What's more likely is that the Republicans will dwindle to the status of regional party based in the South and Great Plains for a few elections while they try and get something worked out. The Democrats held this status in the 1920s, remaining a political force in the South only; after the Great Depression swung the balance of power back to the Democrats, the Republicans camped out in New England and the Great Plains until after WWII.
Additionally, there seems to be this strange law in American politics that no presidential candidate can ever get more than about 60% of the vote, no matter how out-of-touch the opponent is. Roosevelt got 60.8% in 1936; Johnson got 61.1% in 1964; Nixon got 60.7% in 1972; and Reagan got 58.8% in 1984. Since then nobody's even cracked 55%. So, assuming that the two-party system holds, the GOP is going to win about 40% of the vote even in a year when they get absolutely walloped, and they'd only need to drag 10% of the electorate away from the Democrats to bring the situation back to balance again. I think once a couple of contentious issues for the GOP become accepted as the "new normal"- disliked, but irreversible (Obamacare and immigration reform are the most likely candidates)- they'll start putting forth some constructive proposals again instead of just shouting "no!" at absolutely anything the Democrats want to get passed.