If people become convinced that our government will end up printing money (coin) to cover intractable deficits, they will see inflation in the future and so will try to get rid of dollars today, driving up the prices of goods, services, and eventually wages across the entire economy. This would amount to a "run" on the dollar. As with a bank run, we would not be able to tell ahead of time when such an event would occur. But our economy will be primed for it as long as our fiscal trajectory is unsustainable.
Needless to say, such a run would unleash financial chaos and renewed recession. It would yield stagflation, not the inflation-fueled boomlet that some economists hope for. And there would be essentially nothing the Federal Reserve could do to stop it.