Actually the antipathy of the Tea Party patriots against the republican establishment is what attracts the crucial Independents.
Independent voter registrations were 24% in 2012 and catapulted to 42% in 2014. It was the Independents that crushed the democrats in the 2014 elections.
Independents do not like republican establishment types and loath them as much as they loath democrats.
The idea of a 3rd (2nd) party is an idea whose time may have come because of the Independent vote.
Ted Cruz can win by a landslide in 2016 with the Independents. They don’t see Ted so much as a republican as they see him as anti-establishment and that folds perfectly within the views of Independent voters.
Tens of millions of Democrat voters will never ever vote for a Republican, but they would vote for a populist, constitutionalist conservative. UKIP in Britain in a recent election pulled around 40% from the Conservatives and about the same from the Labour voters. Labour voters said they’d never vote Tory. Never.