They love martyrdom. They'd rather lose than compromise.
They'll stand for the same old things, transferring wealth to the wealthy and fighting wars for the benefit of mega-corporations with the bodies of the unemployable.
As for a leader, they'll come up with a suit who will be the mouthpiece of the folks who run the party. They are not very visible, but the elected folks dance to their tunes. An independent Republican is as rare as a one-second steak.