Trump can't keep the shutdown going for years. He's not an Emperor, and even if he were, he'd wind up like Caesar long before then.
They'll make a stubborn show of defiance but in due course some deal will be struck and some defections will occur because holding the government hostage to fund a wall to keep the Mexicans out is insane. Trump may be willing to fight to the bitter end for that but I guarantee no career Republican politician is.