"Top 1% pay more income tax than bottom 90%!"
"The top 1 percent of tax returns paid 38 percent of all federal income taxes"
"Top 0.1 Percent pays more income tax than bottom 80 percent"
Now, it seems that much of the difference in tax paid is accounted for by income differences but it still seems that the federal income tax is reasonably progressive (not a bad thing). So it would seem the right has a point, however the point is exaggerated due to the fact they don't mention shares of income and that progressive taxes are not necessarily a bad thing.
You might suspect there is more however (you'd be right). Let's have a look at ALL taxes not just federal income taxes. Other taxes (e.g. sales taxes) tend to be much more regressive (poorer people spend a higher percentage on goods/services), so how do they change the picture. Well, here are the figures:
As you can see they paint an interesting picture. The total tax liability of each income groups is roughly identical to their income share with some element of progressiveness. This radically changes the policy implications however. If we were to change the federal tax system (as is suggested by the right) then we may very well end up with a system that is regressive (not a good thing at all). The point to take away from this is (apart from the data manipulation of the right) is the fact that the tax system is not highly 'unfair' to the rich.
For completion I also include the total effective tax rates of income groups (right). For more info I recommend Citizens for Tax Justice and in particular this report which has more up to date figures which show much the same picture.
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