This is simple, the Republicans will move to the left, and a new party will form on the right.
I am a Republican because it is the only balance to the Democrats. Once I am sure the Democrats are no longer a major polictical party, I will find a home in a party that is to the right of the current Republican party.
The Dem Party will not just fade away; it will be replaced and the GOP will still need your support. And a faaaaaaaar right party will NOT have any more of a chance, then, than it does now.