Another option, less overhead-intensive, would be to exempt the poorest from all sales tax, and have a card you show the register to establish examption. A food-stamp card you're paying with would automatically qualify. Of course, groceries are already exempt from sales tax in any halfway sane jurisdiction, so never mine.
Actually, everything is already exempt from sales tax in any halfway sane jurisdiction (there are just very few halfway sane jurisdictions). It seems to work fine for Oregon, so let's just eliminate it instead of trying to patch it. :)
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Pardon my typo in the previous comment; I'd fix it if I could.