Where would this cash come from? Right now, banks get it from the mints, which print it on a demand basis. And even if you use cash for most of your transactions, if you keep your money in the bank...
My best guess to this would be the government would have to temporarily (or permanently) set up a federal bank that would get the cash out, perhaps giving back a larger amount than normal that year in tax returns that have to be picked up in cash from said bank. New problems would need new solutions.