Poor people already pay next to nothing in taxes - the bottom 60% of society, making less than $50k only contributes 7% of total tax revenue from income taxes, while 0.3% of those making more than $1M per year contributes 27%. [1]
I think the US has pretty good revenue structure in that regard. In my country 62% of federal budget comes from sales taxes (e.g. 23% VAT), which disproportionately affects poor people.
[1] https://www.stlouisfed.org/on-the-economy/2017/january/feder...