That's where I differ on how the FairTax handles such a thing. Many states which impose retail sales taxes exempt things like unprepared food, clothing, medicines, and services which are considered life critical. The FairTax gives each household a "prebate" which covers the costs of these taxes for everyone. I believe the prebate is unworkable given that our government can't really do anything right, so I prefer this approach instead. The approach of exempting certain items from the tax also prevents the government from stealing your prebate just in case you decide you do not want to buy the health insurance that it thinks you should buy.
But for people who can afford to pay for things like $200 Nikes, the latest and greatest Smartphones, cable TV, broadband Internet, and other such luxuries, but who otherwise do not pay federal tax, they can afford to pay something towards the cost of government.
The point is that, once you start getting into the details of which categories should be exempt, the same thorny issues arise, and you are end up with something unwieldy if you consider them or something unwise or unfair if you don't.
Oh, and I forgot to add: a poor person will spend a greater proportion on taxes even if you exempt food. The original question remains unanswered thus.