Are you sure? Gas consumption is notoriously inelastic. West coast gasoline is already a dollar or more than it costs on the east coast. Do poor people drive less in California than in Florida?
If you want proof of this, just look at what happens to sales of large vs small cars when the price of gas changes.
https://ww2.arb.ca.gov/our-work/programs/fuels-enforcment-pr...