I think the sheer fact that they've made this play alone would draw enough support away from Trump and Cruz (or whoever) such that Hillary would win enough EVs to keep the matter out of the house.
You'd think this, but that didn't stop Truman in 1948. Truman had the Dixiecrat challenge, and the Henry Wallace challenge.
While it wasn't stated in the OP explicitly, I feel as though this would only be possible nowadays via some sort of centralized effort from the GOP establishment. Especially if it were clear to the media that the end goal was winning the presidency in the House, I think it would hurt the GOP name a lot (if it hasn't been already). In this sense it seems different from 1948 to me.
