AtlanticBlog has a very nice post on why we might not want to replace a progressive income tax with a flat tax. Citing a book by Eric Rasmussen and Frank Buckley, and a recent paper by Gary Becker and Casey Mulligan, Professor Sjostrom raises the possibility that a flat tax would actually make it easier for the government to deprive businesses and the public of their income. (I believe, but can't find the cite at the moment, that Steven Landsburg also raises this possibility in his wonderful book, The Armchair Economist.)
I think that this argument is sound. But as with the vast majority of economic arguments regarding public policy, we need empirical evidence. I still think it would be worth taking the risk to try a flatter tax. (Maybe somebody has already tried to tease out the effects by comparing the progressivity of different states' tax structures?)
UPDATE: Professor Sjostrom reports that Landsburg's anti-flat-tax argument does not appear in The Armchair Economist. But I've found where it does appear: http://slate.msn.com/id/2030.