The problem I see with a federally administered "fair tax" idea is the effort to find a "one size fits all" solution. It seems every time a "one-size-fits-all" approach has been tried for any issue, we wind up with a "one-size-fits-none" solution.
Over time, as new politicos replace old, any tax system that is controlled by the Feds will be dorked with until we are (eventually) in a mess similar to what we have today.
I like the idea that the Feds don't tax individuals or businesses directly. The Feds levy a tax on the states as a percentage of the state's GDP. It is left entirely up to each state how they collect the revenue to pay the state's federal tax bill.
Each state can have their own policy (flat tax here, sales tax there, status-quo elsewhere). Within 5 to 10 years, it should be evident which states have the most desireable policies by the increase in residents and businesses.