2) Another big chunk of the working population would lose their jobs because their industry gets shaken up: Those working in polluting industries (coal and gas) or the huge part of the economy that's surrounding petro-chemicals (gas stations clerks, heating engineers, fuel truck drivers), etc.
You would need to redistribute the CO2 tax income as welfare checks but again: That's not a politically viable solution because the fear of job losses pretty much outweighs anything else.