The federal tax code...

...may not be as progressive as you thought. According to Ezra Klein's blog (my emphasis):

The Congressional Budget Office collects data on the "total effective federal tax rate." That's the tax rate that people actually pay to fund the federal government. It includes not just income taxes, and capital gains, but payrolls taxes and excise taxes. And what it shows is that the tax code is progressive at the lowest levels and regressive at the highest levels. The middle class, however, ends up having a bad time of it.

In 2007, taxpayers making less than $34,000 paid a 6.4 percent tax rate. Those making between $34,000 and $50,000 paid 13.5 percent. between $50,000 and $75,000, the rate rose to 16.3 percent. So far, so progressive.

But then the progressivity just...stops. If you make $75,000 to $103,00, you're paying 20.8 percent. If you're making between $103,000 and $142,000, you're paying 21 percent. If you're making between $142,000 and $353,000, you're also paying 21 percent. If you're making more than $353,000, your tax rate actually falls a bit, to 20.7 percent. And if you're one of the 400 richest taxpayers in America, your rate falls all the way down to 16.6 percent -- in no small part due to capital gains taxation.

This, by the way, actually overstates the progressivity of the total taxes most Americans pay, as state and local tends to be more regressive. Add them in and the share of the tax burden paid by the poor and middle class rises.