A solution to this quandary was figured out in 2011. Due to a quirk in the laws, the US Government has the ability to issue platinum coins of any value. These 'coins' never have to be paid back. The U.S.'s national debt could be retired by minting a couple "trillion dollar coins":
https://en.wikipedia.org/wiki/Trillion_dollar_coin
The Federal Reserve does a decent job at keeping the money supply growing at less than a hyper-inflationary rate, but the value of our money has collapsed since I was a kid, since we all were kids...