The problem with that is the republicans would look bad and very petulant for doing this.
The only leverage Obama has are the middle class Bush cuts. So why not bite the bullet pass those and then if you do not come to the table we will not raise the debt ceiling. Take away their ammo and then see we compromised. That is the only way to make him own it so to speak.
I do not agree that the republicans would look petulant. Otherwise we have been petulant since the bill was passed about 10 years ago. Obama is the one who said we should not raise taxes in a down economy. Well, here we are in a more down economy than when he said it. Obama would be the duplicitous one. Call his bluff. We have economic cancer. If we do not tackle it now it will complete the destruction.