The claim that only rich people pay taxes is a zombie lie — something that keeps coming back no matter how many times it’s killed by evidence.
So, let’s try another shot to the head.
Yes, high-income people pay the bulk of the federal income tax. But that’s not the only tax! And while the income tax is quite progressive, the payroll tax — the other major federal tax — isn’t; and state and local taxes are strongly regressive.
Citizens for Tax Justice (pdf) has the goods: combining all taxes, federal, state, and local, we get this.