"shift towards"? The Republican party has been fundamentalist by all but American standards, and I'm not even talking about the more extreme tea party folks. Those are just plain insane.
Sounds like he means fundamentalist in the religious sense. Believe it or not the evolution of the neo-con and American Christianity's attachment of itself to the GOP is a pretty recent development. Not long ago an average Republican was mainly fiscally conservative and the "family values" types were the outliers.