If the Debt Limit was already reached in May, how are we paying bills till August?

Back in May, we hit the debt limit.  Yes, May, not August.   But Treasury Secretary Timothy Geithner used "extraordinary measures" to delay the problem.

Basically what he did was to stop selling bonds to various government agencies - both local and federal.

This has a huge effect because over 40% of the US national debt is in fact held by various American government agencies.  Social Security alone holds $2.6 of the $14.3 trillion out there, but Social Security is still buying US treasuries because of legal requirements (it can not invest in anything else).   It is other organizations, such as the Federal Employees Retirement Funds (it used to hold about $783 billion in treasuries, but not anymore), that are buying things besides treasuries.  As their existing bonds come due, the government is paying them off and not issuing new bonds.  Presumably those agencies are using that money to buy municipal and corporate AAA bonds.

Note that the government is paying them off.  You see, the USA ran out of debt in May, not cash.  In fact, we just got an influx of cash in April.  It has the cash, it simply does not have the legal right to sell more bonds.

The problem is, eventually that cash will run out.  The cash we are paying out now was supposed to last us a while, but that assumed we would be selling more bonds.   Each day, we spend more than we take in (deficit, definition of), so eventually that money will go away.

The Fed thinks it will all be gone on Aug 2.  God help us all.