"Deem and Pass" was the technique used to pass HCR where a bill is passed without the House actually voting to pass it. This is the technique Michele Bachmann and similar great minds told us was so unconstitutional that it threatened the very existence of the space-time continuum and was so bad that even Conservatism Itself could be threatened by it.
Guess what the debt ceiling deal includes? A deem and pass of the 2012 budget. Which is to say - the 2012 budget cannot be taken hostage by the House.
And since the 2012 budget is a budget, it is subject to the usual anti-filibuster rules of any other budget. Therefore - the 2012 budget cannot be taken hostage by the Republicans in the Senate.
FWIW, the 2012 budget includes $7B in spending cuts. The other $963B occur in later budgets. So the impact on the economy ought to be minimal as well.