They're secured (not quite backed) by inability to do certain kinds of math. That's proven to be moderately reliable over the years (cryptosystems get weakened and replaced, but usually not compromised abruptly) but certainly catastrophic failure of a cryptosystem has happened more often since WWII than has catastrophic failure of the US Government.

All of that said, I'm not convinced government use (also not quite backing) is such a big deal - I've pointed several times now to the recent Economist article about the Somali Shilling retaining value decades after the issuing government collapsed.