You can only postulate this if you also postulate he was dumb as a box of rocks to believe what the Democrats told him. I think he knew exactly what would happen, but for public consumption apparently "believed" the Democrat deal to placate his voters - didn't work. The voters saw through the bullsh!t. You actually think that Bush BELIEVED that the Democrats would cut spending if he signed the tax increase? Does anyone really believe that a Washington insider was that naïve?
We could eliminate 10% of the government TOMORROW and no one will notice. A shutdown is needed to show just that. Could be on par with the firing of the air traffic controllers in regard to our enemies.