OK, let's catastrophize for a moment, in a vein that I hope will seem completely misguided by a couple of days from now. But while the probability of this may be low, I don't think it's zero.
Suppose the House Republicans pass a bill with ransom demands and then leave town (or else simply refuse to accede to anything without ransom). Say the Senate and White House reject these demands, and the result is a debt limit breach, and that this in turn has very clear bad consequences. At this point, having triggered the unforgivable, all the House Republicans could really do is double down, such as by blaming the other side for rejecting their "reasonable compromise" and accusing the Obama Administration and the Treasury of deliberately mishandling the post-breach cash flows.
Indeed, if House Republicans accept the logic of unavoidable escalation, it is hard to see where they would stop. Impeachment? Charges of "economic treason"? Sometimes the best defense is a good offense, or at least it may feel that way in the heat of battle. And tribalism being what it is (an argument that applies, of course, to all sides), they would definitely have supporters, no matter how far they went. In short, this could get very ugly indeed.
We are used to having the parties spin alternate histories, where "we" tried to do good things but "they" messed everything up. But if what's happened is really unforgivably bad, and if it clearly reflected a major social breakdown amid dueling accusations of fundamentally antisocial behavior, we could end up in a place where the United States has never been before, other than from 1861 through 1865. And as examples such as World War I show, this can happen startlingly fast, and without anyone's having expected it, quite simply from the logic of dueling escalation.