The wannabe 'Pubs will cave in to the King.
Basically only half the GOP Reps are connected to the Tea Party, which makes them a force, but not one which can actually stop something that has been negotiated by the leadership in both parties. Also just to be coldly realistic about it, a very large majority of Congress does ultimately agree that default is unacceptable, not just economically, but in the political price they would have to pay for it with the Centrist voters. Both left and right know they're out on their asses if their only backers are their hardcore base voters (Except for a few rare House districts that are completely dominated by the base). The real question reduces to how little each can give up.