The Bipartisan Policy Center released a Debt Ceiling Analysis today showing that even if Congress does not raise the debt ceiling by August 2nd, the federal government would still have enough incoming revenue to pay: all interest on Treasury securities (thus avoiding default), all Social Security obligations, all Medicare and Medicaid obligations, all Defense contractor bills, all Veterans payments, and all active duty troops, and still have almost $7 billion left over for other items.
The report does note that "inflows and outflows do not match up well and are quite lumpy," but they do assume that "Treasury would nonetheless be forced to attempt to prioritize payments despite the difficulty of doing so." Overall, federal spending would be cut by 44 percent for the month of August which would cause "widespread uncertainty as decisions are made day by day."
Treasury Secretary Tim Geithner does not have to decide whether or not he wants to default on our debt until August 15th. That is the day that the Treasury is obligated to pay $29 billion in interest on previously issued debt.