I'm not sure anyone knows how it'll work. The House hasn't been called on to pick the President since the nasty deal that ended Reconstruction (like 1872 or something). There may be rules written down, but there's no institutional memory to draw on. At this point, as much as I'd like to not live in Donald Trump's America, I really don't know what the better result for the republic would be. I won't shed a tear for him if he isn't picked, but I'm also a little afraid of the consequences.
I made a similar point of being hesitant to jump on the Stein recount effort for fear that a reversal so back channel and legalistic would be destabilizing enough to outweigh the benefits of a non-Trump presidency. I guess there's some comfort in knowing that all of this completely out of our hands right now. What'll happen will happen. #seriousseason