Not really. Despite what Willie Green cut-and-paste above, taxes are indeed an embedded cost in everything that is sold today. That same lower income person is already paying 20% or more, on average, in the price of everything he or she buys, due to the cascading effects of income taxes (which act as a subtraction-method value added tax).
Even still, the sales tax proposals that have been floated go further to address that potential problem. There are basically two potential avenues for redressing apparent "regressiveness" in the system: 1) exempt items that can be classified as "necessities", or 2) provide some form of rebate or allowance to offset the costs of taxes on subsistence-level spending.
I'm personally in favor of the Americans for Fair Taxation's (AFFT) "FairTax" plan, which takes the latter approach. The "FairTax" has been introduced in the House of Representatives as HR 2525. Most questions regarding a national sales tax can be answered by reading the materials on that site -- and there's a committed group of FReepers that will be more than happy to address other questions.