It's a tax on buying. Think about that for a moment. Fair Tax proponents claim that the current tax system causes disincentives for things like exports and U.S. manufacturing. Why would the Fair Tax proposal then not cause a disincentive on the demand side of the economy? ("How will the plan affect economic growth" in the FAQ clearly espouses a particular economic ideology that has yet to be supported by any of the facts of history.)
It also places the entire tax burden on the consumer. Annual pre-tax corporate profits are somewhere between $800 billion and $2 trillion, depending on which data you decide to believe. Why is all that money being left on the table in favor of drawing the entire national budget from consumers?