Just when you think wingnuts couldn't get any stupider.
1. It's not called the "debt limit" -- it's called the debt ceiling.
2. The debt ceiling is raised to pay expenditures already committed to, not future ones.
The process of setting the debt ceiling is separate and distinct from the regular process of financing government operations, and raising the debt ceiling does not have any direct impact on the budget deficit. The US government proposes a federal budget every year, which must be approved by Congress. This budget details projected tax collections and outlays and, if there is a budget deficit, the amount of borrowing the government would have to do in that fiscal year. A vote to increase the debt ceiling is, therefore, usually treated as a formality, needed to continue spending that has already been approved previously by the Congress and the President.
You'd think someone who served in the White House would know this stuff. Then again, it was the Bush White House, so...