By either exempting the first $X of purchases (the way the FairTax does) or exempting certain purchase from a national sales tax, you do prevent the poor from paying tax. Of course, most of us define a poor person as someone who, if he can buy anything, can afford only the most basic of essentials. Far from harming such people, both my proposal and the FairTax would help these people because there would be no federal tax withheld from such persons' paychecks.
Under either proposal though, anyone who would make a purchase that would result in paying either a national retail sales tax, or the amount of sales tax charged under the FairTax beyond the level of prebate, isn't poor.
Consider a person with income Y. You exempt the first X of purchases P from the sales tax and tax the remainder at the rate R. The person thus pays R(P-X) in taxes, that is, proportion R (P-X) /Y of her income.
Regardless of what X is, this proportion decreases with Y: wealthier people smaller proportion of their income.
This is the main argument against the sales tax. How are you going to persuade people that you are right if you don't address this concern?