I'd bet against Obeyme upstaging Republicans with a tax cut. Higher taxes are his nirvana and the only way to pay for what he wants. Of course, the middle class is where are all the money is.
If he did, Republicans could pretty easily co-opt it , or take credit for it.
They're only play is huge spending cuts in exchange for a small debt limit increase.
I could see obama doing it. Part of his and the dems goals is to destroy the Republican party. Besides, obama never intends to pay for any of his spending. Hence the huge defecit.