That would be a political killer. Imagine how Democrats would say that everyone pays the same rate for sales tax. Why do high income earners get larger accounts than low income earners? Their disingenuousness would rival that of the "Fair Tax" supporters.
I expect you're right in terms of how it will be spun, however, the fact that wealthy people consume more than poorer people, would indicate they would pay more taxes. Further, the FairTax would spread the burden of funding SS from a limited base of wage earners, such that imports, foreigners (legal and illegal), and those who do not report or pay under the current sytem, would share some of that burden.