@Cruiser
Sorry, I may be a little late getting back to this but several of the answers that have been given address my thoughts on the situation. The rancor between the two factions is at a point where, in my opinion, they cannot be brought back together. It is a lose – lose situation and whoever takes this job will receive the blame when they fail.
Look at it this way, If he even thinks about compromising, the Tea Baggers will call for his ouster immediately. I am not sure they will even vote him in unless he swears not to consider it. If he doesn’t compromise then we are once again at an impasse and the majority of the Republicans, those who do view compromise as a necessary evil, will blame him for not doing so. Knowing he will not be able to use the compromise/mediation approach he is known for thus limiting his ability to accomplish anything why would he want to subject himself to this abuse?
Best approach the majority Republicans could take would be to work with the Democrats to get a Speaker amenable to both and install him despite the vitriol of the Tea Party caucus. And, maybe this is the approach Ryan is considering but that will leave him fighting both the Democrats and worse still the Tea Party during his Presidential bid and the Tea Party will be much more willing to gut him and leave him hanging with his entrails splayed all over the ground than the Democrats would.
The Tea Party is the ISIS of American Politics right now. They will destroy anything that they disagree with regardless.
If he is smart, he will stay on the sidelines, let the Tea Party install one of their own (someone like Bill Flores) and watch him go down in flames.