Where’s the extra supply going to come from? Last I heard, North America’s refineries are running at full capacity.
Usually suppliers are at least somewhat price responsive.
Refiners can shift between outputs to some extent: eg, they can produce less home heating oil and more gasoline. Alternatively, gasoline can be imported directly, though I understand that this is expensive.
In the extreme case, if refiners are already producing the absolutely maximum amount of gasoline that they can, (the supply curve is vertical and therefore cannot be shift) then I would expect a drop in the tax to be offset by… an increase in before-tax prices. If the after-tax price were lower, demand would exceed available supply and the price would be bid back up.
… which admittedly was what Rysto initially postulated. Whether existing supply conditions would permit increased gasoline supplies for a 20 cent price increase over, say, 3 months (as I’ve speculated) is an empirical question.