Food stamps are done by grants to states.  Each state administers their own systems of redemption.  It is handled through a credit card system and merchants are responsible for ensuring that the credit is used for eligible food items.

The funds used for those are like credit cards in that they are dollars made up out of thin air.  Any credits not used just simply disappear.

With bitcoin those funds would have to exist in an escrow so that any credits not used would return to the pool.  So instead of a card holding a specified amount of btc that it would be authorized to draw a specified amount from the pool.  That part is manageable in software.

Currently the national budget for food stamps, actually called SNAP btw. is pushing 100 billion.  The exchange rate for the existing 12 million btc would have to skyrocket just cover snap.

As bitcoin grows in usage with merchants the exchange rate naturally align itself.  Using the force of Government to mainstream BTC would be the kiss of death.