Predictions are hard, especially about the future, but I think this is right:
If Schelling is right, one might plausibly expect the next few days of negotiations to be shaped by two contradictory forces. On the one hand, House and Senate Democrats and the White House are likely to hang tough, because they anticipate that the House Republicans will have no choice but to fold. On the other hand, the House Republicans may have a strong incentive to double down, because they fear that if they concede this time around, their future leverage (including their leverage over the debt ceiling negotiations) will dwindle rapidly. This may give further reason to Republican moderates not to dissent from the party line (they may not like that line: but they do not want to damage their party’s negotiating strength).
The GOP may eventually fold on this, but I expect a double shot of Wolverines! over the next few days.