The cynical view on this is your currency to an extent is not only backed by your economy but also by economic resource you can take by force which in case of US is ... I obviously do not want to simplify this to a single factor of mil. power but it's definitely an important aspect.
If people believe there's a currency crisis and that the currency will crash, it becomes a self-fulfilling prophecy. They would instantly convert dollars to another type of currency or goods they think would retain value. They would take their entire paycheck every month and buy any possible physical good they can the same day to try to keep the value. You can have the largest military in the world, the currency would still crash like a rock, trust is everything for a currency.
