Since the mid-90s, the plank of the Republican party has moved towards the center--think gay marriage, for instance--and the Democrats have moved wildly left. Whenever people think the Republicans have moved to the right, I ask them, "on what issue?" I can show you an issue where the Democrats have certainly moved to the far left in the past 20 years or so; heck, maybe they've moved crazy left in the past dozen years or so:
President Bill Clinton, 1995
Senator Barack Obama, 2005
I've pointed this out earlier this year, here. That link includes yet another video, of President Obama, talking about illegal immigration.
What was eminently reasonable just a few years ago, and had been reasonable since the founding of the republic, is now considered wrong/racist/evil/stupid/etc. It's not Republicans who have changed position here.