This interesting paradox happens when a politician becomes "compromised" and quickly finds out which side of their bread is buttered. Most of our politicos are puppets for special interests. Their only real skill is making it look like they are working for their constituants when they aren't.
And they've gotten real good at it too. But eventually the GOP will have to start listening to its constituents on this issue or they're outta there. Their "outreach" to illegal aliens in order to widen the tent is turning off more people than they realize. These same type policies is what's causing so many to flee the democratic party.
If a third party truly rises up in the country, it will be because of this one issue and all the issues surrounding it... ie housing, education, crime, and on and on.