Forum

the U.S. government now owes more dollars than actually exist.

So why doesn’t the U.S. government just fire up the printing presses and print a bunch of money to pay off the debt?

The U.S. government does not issue U.S. currency - the Federal Reserve does.

So, when the U.S. government needs to borrow more money (which happens a lot these days) it goes over to the Federal Reserve and asks them for some more green pieces of paper called Federal Reserve Notes. 

The Federal Reserve swaps these green pieces of paper for pink pieces of paper called U.S. Treasury bonds. The Federal Reserve either sells these U.S. Treasury bonds or they keep the bonds for themselves (which happens a lot these days).

So that is how the U.S. government gets more green pieces of paper called “U.S. dollars” to put into circulation. But by doing so, they get themselves into even more debt which they will owe even more interest on.

etc.
http://theeconomiccollapseblog.com/archives/it-is-now-mathematically-impossible-to-pay-off-the-u-s-national-debt