The usual complaint about flat taxes is that they don't generate as much revenue, which results in a higher base rate. That, right or wrong, ends up sounding like a hike on low income people that can afford it least. The math on that argument tends to be a little shaky, but it "sounds reasonable" and the people that usually support a flat tax are righties that promptly get tarred as "eat the poor" demons by the other side of the aisle.