Effective Federal Income tax rates:

Lowest Quintile.....-11%
2nd Quintile...........-1%
Middle Quintile.......3%
4th Quintile.............7%
Top Quintile............16%
Top 1%...................24%
All Quintiles.............10%

"Wait, the middle class also pays medicare and social security taxes" you say...? Sure, but they also get a medicare benefit that is 3-4x what they pay in, and they also get a SS benefit that is subsidized by... you guessed it, high earners.

Still, if you want to look at all federal taxes (while ignoring the subsidized benefits that the middle class gets), here you go:

Lowest Quintile.....2%
2nd Quintile...........9%
Middle Quintile......14%
4th Quintile............18%
Top Quintile............27%
Top 1%...................33%
All Quintiles............21%

So even if you include ALL federal taxes (income, payroll, excise, etc), the top 1% pays taxes at a rate that is almost 2.5x that of the middle quintile. For just income taxes, the top 1%'s burden is 8x that of the middle quintile.

You can argue that the rich SHOULD pay more as a percent and their income (and I'd agree), but to argue that "the disproportionate tax burden falls on the squeezed middle class" is to either ignore the facts, or to ignore the meaning of the word "disproportionate"