Your not getting it. The US doesn't "pay" anything. They discharge debts via tendering paper promises. It doesn't matter what the US owes. As long as people accept as valuable the paper, the debt is discharged.
Perhaps I'm wrong, but given U.S Treasuries are denominated in 'Reserve Promises'. If there are not enough 'reserve promises' in circulation, then that is a default.
The only way to get a true default is to perform a notarial presentment and see get a certificate of protest for non-payment/non-acceptance. AFAIK T-bills and T-Bonds are all in electronic format now. The law has not been update to give the same type of rights and remedies as a signed and/or sealed promise in writing.