As far as I know gas tax isn't paid by the producers, but sure we can combine gas producers and users for this discussion. Money taken or given to either one has the same effect on the demand for gas production.
When that $x in taxes is paying for the infrastructure used, then the gas producers/users are actually getting $y+x from the government. The $x, being a service charge, cancels out, and the only thing left is $y. $y is the difference between the world we live in vs. a world where the government paid no special attention to the industry. It's the most important number.