Looking around the Web today, most grassroots conservatives and a frightening number of Republican members of Congress seem to be under the misapprehension that raising the debt ceiling increases government spending or that failing to raise it decreases government spending. Neither is true. I don't think anyone really knows what will happen if the debt ceiling isn't raised, but a reduction in government spending is not one of the possible consequences.
There are two kinds of government spending—mandatory and discretionary—and neither of them will be cut by a single penny by a refusal to hike the debt ceiling.
Mandatory spending is Social Security, Medicare, Medicaid, some farm subsidies, most of Obamacare, and a few other things. The way "mandatory" spending works is that the law specifies some eligibility rules for who gets money and how much and then the spending just keeps on flowing until Congress steps in and changes the law.
Discretionary spending is the military, the salaries and benefits of federal civilian employees, and the whole broad range of small-bore programs the government runs. The way "discretionary" spending works is that Congress appropriates such-and-such amount to be spent over such-and-such a time horizon, and then absent a new appropriation there's no more money to spend.
The debt ceiling has zero impact on either the appropriations process or the Social Security Act and other major pieces of entitlement spending. Those laws are all on the books, and those are the laws that determine the volume and pace of government spending. As a separate matter, we also have tax laws that bring money in to the government. Then we also have a borrowing process through which Treasury can plug the gap between the money it's legally entitled to collect and the money it's legally required to spend. A failure to raise the debt ceiling would seek to make it illegal for Treasury to plug the gap. But it wouldn't alter the legal requirement to spend. It's unclear what happens next. Treausury could ignore the debt ceiling and orchestrate an "illegal" bond sale, thus accruing debts outside the debt ceiling. Alternatively, Treasury could try to find a way to "pay" some of the government's bills with IOU notes rather than money, which would be another way of accruing debts outside the debt ceiling. Or Treasury could simply not pay everyone what they're owed. But if you don't pay a doctor what he's owed for services rendered to an elderly woman with Medicare benefits, that doesn't change the fact that you still owe the doctor his money. It's just another way of accruing debts outside the debt ceiling.
But there is no option whereby the failure to raise the debt ceiling reduces the government's obligation to spend. Spending is determined by the laws that have already been passed, and if you want to spend less money you need to change those laws.
Read more of Slate's coverage of the debt ceiling fight here.