A new report from Citizens for Tax Justice, a left-leaning tax analysis shop, does all that. Overall, CTJ finds that the tax code is still progressive, but much more mildly so than you might think:
The bottom 80 percent of the income distribution pays less than their share of income, but not a whole lot less. And interestingly, the 20th through 60th percentiles get a bigger break than the poorest 20 percent. The tax code has a bias for the middle-class over the poor, in other words.
And while the richest Americans pay more than their share of income in taxes, the margins aren't dramatic. The top one percent pays 24 percent of all taxes but makes 21.9 percent of the money. Particularly if you believe that money quickly loses its value the further you go up the income ladder, a conclusion which the happiness economics literature tends to support (that's why papers like this tend to look at the log of income), that's not that progressive a system.
Overall, the American system remains the most progressive tax system in the developed world, whereas most social democracies like France, Germany and Sweden have actively regressive systems heavily reliant on value-added taxes. Then again, U.S. pay-outs aren't nearly as progressive, and so our government reduces inequality through taxes and transfers much less than peer countries.