First we have to get clear two different concepts. the tax burden is taxes as a share of the taxpayer's income. the tax share is one person or group's taxes as a share of all taxes. The right likes to confuse the latter with the former. Burden speaks to fairness. Share, in my view, does not in a direct way. Shares of income, before or after tax, speak to fairness.
Tax burdens have been fairly stable over time. Shares move as income distribution changes, which has been a lot in recent decades.
Federal taxes - rich pay more in terms of burden and share State tax burdens are more even over income classes, so the share paid by rich would be higher on this account (for equal sized groups).
All taxes put together have been found to have the famous 'soupbowl' pattern: slightly higher burdens at both ends (poor and rich), but similar for the vast bulk of taxpayers in between. So it is possible for a poor family to pay more in terms of tax burden than a much better-off family. But this is so only including state and local taxes, and then not for very many families, and not by very much (in terms of percent of income).
There is very little change in burdens in the U.S. over the past twenty-five years. The share and burden of the rich has bounced around more than other groups, but not outside a very narrow range.
See "State of Working America" for details. There is also a new report from the Congressional Budget Office, free on the web. Author is Frank Sammartino.
MBS