The U.S. isn't going to run out of money and this country isn't Greece despite what Lindsay Graham says.
Moral Obligation Coupons
Don’t like the platinum coin option? Here’s a functionally equivalent alternative: have the Treasury sell pieces of paper labeled “moral obligation coupons”, which declare the intention of the government to redeem these coupons at face value in one year.
It should be clearly stated on the coupons that the government has no, repeat no, legal obligation to pay anything at all; you see, they’re not debt, and therefore don’t count against the debt limit. But that shouldn’t keep them from having substantial market value. Consider, for example, the fact that the government has no legal responsibility for guaranteeing the debt of Fannie and Freddie; nonetheless, it is widely believed that there is an implicit guarantee (because there is!), and this is very much reflected in the price of that debt.
So the government should have no trouble raising a lot of money by selling MOCs. It’s true that if they’re sold on the open market, they would probably sell at a substantial discount from face value, so this would in effect be high-interest-rate financing. But that’s better than either default or giving in to blackmail.
Update: If there is a legal problem even with selling these coupons, there are still alternatives, such as paying suppliers with these coupons and then having the Fed buy them. The mechanics really don’t matter; as long as we’re in a liquidity trap, printing money, printing conventional debt securities, or printing funny money with no legal standing that nonetheless lets the government pay its bills are all equivalent.