Some states already (or used to) do something similar to this. I know certain states put no sales tax on foods purchased in grocery stores, but other states will not tax essentials (foods such as milk, eggs, meat, vegetables, fruit, etc.). Those states do, however, put sales tax on chips and cookies and sodas. Granted, this isn't nearly as steep as a "sin tax" might be.

Note: While doing research on this, I found nothing that supported this, although I do remember sales tax in Minnesota being a little different on individual foods. I did discover a few sites mentioning tax on foods that can not be purchased with food stamps, as well as this link outlining State Sales Tax Rates. It would be interesting to find (and time consuming, I'm sure) what each state has set for sales tax on food purchases.