Identifying the extremists as only Christians isn't accurate. There are many secularists that share the same stage. Militia groups, bigots, etc...
Nor would I give them more than a few percentage points of influence. Certainly they have nowhere near to a clean 1/3rd of the ear of the Party. For the most part they are ignored by everyone except the MSM that loves to stir a certain image of Republicans/Christians to the masses.
I agree to a point with your media assesment. However,remember GW needed everyone of those votes. A win of about 2.5% of the popular vote shows how important those votes were. In Ohio, there was close co-ordination with the leaders of the anti-gay marriage admendment.