Douthat calls the flat tax a "fantasy":
A Republican politician could have all the eloquence, charm and charisma in the world, and he still wouldn’t be able to sell the American public — or even, I suspect, the Republican electorate, Herman Cain’s current poll numbers notwithstanding — on the notion that their own taxes should go up to pay for a tax cut for the top 10 or 5 or 1 percent of earners. (It’s fun to imagine the attack ads: “Rick Perry: He’s Ronald Reagan for the rich, and Walter Mondale for the rest of you.)
But a simpler tax? With, say, three rates? A post-card tax return that kills the lobbying industry? Sellable. I'd buy in a heartbeat.