Obviously, Republicans (and here l mean the party not necessarily the people that vote for it) are not philosophical nihilists. But I do not believe that they stand for anything except winning elections.
Democrats sincerely attempt to govern, and often end up doing it poorly. Republicans govern poorly by design and call it "smaller government"...with the notable and notably expensive exception of the military, where no expenditure is too lavish, no mission beyond our grasp, and no criticism acceptable within the bounds of loyalty.
Nihilistic? Maybe not quite. But deeply cynical and dangerously destructive? You bet.