Let's be honest, everyone huffs and puffs around this but don't have a handle on the facts. Look here[0]. The US is by far the one of the largest GHG producer per capita, and this is not a pinko anti-American bit, it's solely the US, not Europe when taking to account total emissions and emissions per capita. The US is second on the total scale of emissions per year, and not shown here (can't find the link) but first in terms of cumulative positions over the years, but it's a good thing to remember that China expends a lot of their emissions to produce things we consume.
A carbon tax would be regressive for the American middle class. On the other hand, it would in fact be beneficial for the global south/poor. That is one of the difficult things about this, because a carbon tax would hit the middle class (note I didn't say working class) in the US which has quite a bit of power globally through their ability to elect the US president, so implementing any sort of carbon tax without giving them some deal will be moot politically. It would hit the working poor in the US pretty hard as well, although a good fraction of them don't own a car[1], so they wouldn't face a tax on the largest source of GHG's in the US.
[0] https://www.ucsusa.org/global-warming/science-and-impacts/sc...
[1] About 19% of people who earn less than 25K per year (yes! very poor) don't own a personal vehicle.
https://www.bts.gov/sites/bts.dot.gov/files/legacy/publicati...