Except part of the problem is that the Federal Government has only a small effect on progressive taxation. The real trouble is the states. What difference does it make if we tax the poor at 0% or even -10% nationally, if the states are crushing them under 15%? 15% of, say, $20k is a fuckload of money to anyone who makes $20k.
More generally, states are where conservative zealots have busted the fuck out of liberal causes in the last couple decades. Bunches of states, especially in the rust belt, vote Democratic in every national election, but can't get fuckall to show up in any non-presidential year, with the effect that these states, MI, PA, WI, OH, e.g., are run like radial right wing monopolies. It's crazy that anyone thinks that sales taxes are a good idea, given that we live in a consumer driven economy. As the conservative warlord Milton Friedman said, if you want less of something, tax it; if you want more, don't. This line of reasoning is one of the many conservative principles that has been completely lost in the modern conservative movement. (Unless of course they took this to mean, "If you want fewer poor people, tax being poor." Doubtful, but with geniuses like Louie Gohmert and Paul Ryan running policy, I suppose I wouldn't discount anything.)