Good read on the different economies at work in the US at The American Prospect. It seems like this could be fixed without directly changing the minimum wage (though that is probably easiest). Since all wages are reported to the government for tax purposes it would be pretty easy to see where people work who receive aid (welfare, Medicaid, food stamps, EITC) and then send supplemental tax bills to those companies. If Wal-Mart employees get $10 billion in tax benefits because they don't get paid enough, then Wal-Mart gets a $10 billion bill from government to cover it...after corportate taxes are paid (i.e. it does not reduce their corporate tax bill, while improved wages would).
Won't happen and would likely be a pain in the ass to implement, but a man can dream. Really though: just raise the minimum wage.