Here's one way to express how catastrophically screwed the U.S. government's finances are: If the entire U.S budget were cut to zero, effective immediately—the military, all entitlements, the electricity bill for the Capitol—there still wouldn't be enough money to cover the payments on old debt that come due every day.
[UPDATE:] Some people have disputed Wilson's results. It's important to understand that the U.S. actually hit its debt limit back in May. Since then it has been paying its bills with cash on hand. Yes, there is money coming in, but it's not a steady flow. It comes in batches. You can see the spikes in Wilson's graph. In the aggregate there is enough money coming in to cover interest payments, but because of the way the timing works out, default is inevitable without at least some additional short-term borrowing. This is serious shit. On August 2 we really do hit the wall hard.