Haven't we seen this movie before?
If a threat to shut the government down and perhaps default on debt could be used to exact serious progress on deficit and debt reduction, I would be all for it. But progress is all that could be hoped for. There is no chance of deficit reduction to zero in time to beat the deadline.
The problem with this game of chicken is that there can be no winner if neither side blinks. It's like the preverbial threat to shoot a hole in the bottom of the boat to punish your adversary. We're all in the boat together.
The side doing the threatening is more likely to be blamed if it goes bad than the side that being threatened. That's what happened in 1995, when the gambit backfired. A better approach would be for the side with the enhanced power and public support to use it as adults and achieve their goal based on its merits rather than try to win a game of chicken.