My guess, from here in Ohio, is he won't step down until at least after the November election, if then. Seems prudent! (for those who missed it, Boehner won his own primary very handily, a couple weeks ago)
But there must be quite a kerfuffle going on right now re: who will become the next House Majority Leader, LOL! Cantor is principled, and a good man, regardless of his shortcomings...you have to give him that at least, IMHO.
Like betraying the Constitution?
Boehner’s problem, like Cantor, isn’t degree of conservatism. Boehner was a pretty reliable vote earlier in his career. He’s sold out to K Street and the consultants, and lacks any political backbone. He’s also ill-suited to be the public voice of a party. He’s simply terrible at it.