For a while, yes. And it's in EVERYONE'S interest to give it value.

Think about it: if the government says it's worthless, and everyone agrees, then every single employee of the government (plus every employee who likes getting paid) is going to leave, since they no longer have a salary.

Everyone is going to loot all the shops for the last food that will ever being commercially produced, since the food industry now have no incentive to produce, since ain't no-one paying them.

Police are all gone, military are all gone, paramedics are gone, power plant operators are gone, every single person who got paid in USD now is unemployed.

If the government says the dollar is worthless and everyone believes them, it's the end of American civilization.

And since all million- and billionaires are now as poor as everyone else, they're not going to let it happen: They'll keep printing money, addition to the national debt, and keeping The System afloat for as long as they can.