Disagree. They'll stick with the party that mostly will carry the single bucket of water they're interested in. Single issue voters will not get what they want if they start up a fringe third party, railing on the one issue that drives them. That's what I think is wrong with single-issue voters who decide that "Ah-HA! I'll join Party X because Party X is "anti-illegal immigration", .... but deep down beneath the surface, they are pro-terrorism.
But if the GOP actually increases the size and scope of the federal government faster than the democrats or any other party, then why would they continue to vote Republican.
Republicans (in their current manifestation) also won't defend the southern border any better than the democrats. They also won't defend property rights. The won't defend freedom of speech either (CFR).