Lets say everyone declares USD is worthless, the government could 1) sell things of value demanding explicitly USD in return. 2) Impede movement or other activities, use of public goods using force and demand a toll explicitly in USD. I.e. this much $ is worth 100km of highway travel. Like calculating the value of a person's life to the government in free health coverage countries based on where they draw the line on spending to keep them alive, I think the value is the inverse of the cost the government would go to to prop it up.
You could argue without money how would they be able to enforce, however enforcement of a government order has not always required money, and that's one hypothetical too deep for me.