You give it back to poor as a income-phased out refundable tax credit. Crucially, base it not on how much they drive or consume, but on their income.
Name it something like the "Worker's Energy Credit". In the worst case, it cancels out the carbon tax spent by them commensurate with their lower income.
In the best case poor people who don't drive much actually come out ahead, and it's just a very progressive sales tax.
The rich might hate it, and call it "redistribution", which is fine because that's exactly what it is, and what taxes have always been, but this one would redistribute downwards instead of upwards, and incentivize lower carbon emissions by those who can afford it.