I'd support repealing it and then later replacing it with something tremendous once we figure out what the hell is going on.
This. Only it needs to be TREMENDOUS!! for accurate feel.
In seriousness, since our system works the way it does, another party containing most of the members of the current GOP would just reappear. We'd have to find a way to get to the heart of the matter with compassion to really fix this issue, and simply doing away with the GOP wouldn't do that.
Unfortunately, though, I'm afraid we're heading towards what Washington (and thus Hamilton and Madison) warned against in his farewell address.
http://avalon.law.yale.edu/18th_century/washing.aspIn my mind, the Constitution has already been negatively affected (the cap on Representatives was one of the worst decisions as it also made the electoral college imbalanced, giving more power to less populated states) as these folks warmed against, and now, as predicted, "unprincipled men" have used the spirit of revenge to gain power and twist the system to their own ends.
I do not know how to fix this issue, but "abolishing" a party without another option would only entrench the members in their desire for one-upmanship and revenge.