Do the US government pay interest to you on your dollar bills? If not I don't see how that is debt. Lots of countries has a currency without paying huge amounts of interest to support it.
Update for clarification - initial response was a bit flippant and not very well considered... Technically phyisical bills ARE debt (they are a liability of the central bank, after all) but they don't _behave_ like debt because they yield 0%.