True, but this isn’t about the budget. Congress has already submitted a budget for 2011. The senate hasn’t submitted budget in 2 years.
If anything, republicans should demand that until the senate puts through it’s budget, the debt ceiling is off the table. Let the president cut out programs.
A budget passed would imply that all the monies needed for the budget are received by revenues or by borrowing. Thus the debt limit is pretty much ignored.