Sometimes you can. A decade or so ago when California ran out of money, they issued warrants to their payees, and lots of banks accepted those at face value.
In practice, most people in the US use credit (which means spending can go unpaid for about 25 days without any costs incurred) and most people bank with a national bank (so they are screwed if all federal employees stop paying back loans at the same time).
That said, food banks are gonna see lots more foot traffic and federal employees might start looking for other work.
Practically speaking, you are correct, but interestingly all dollars are literally an IOU from the US government, so you do buy food with an IOU from their employer. Debt from or to a sovereign is the basis for all money.
