What tax rate would actually produce a noticeable decline in demand?

$4/gal gasoline saw a dramatic turnaround in fuel demand.

"$4/gal gasoline saw a dramatic turnaround in fuel demand."

But that was not a tax. That was market forces. Many thought the market force was 'speculators' and that the price might well go much higher before it went lower.

When a tax is imposed, there needs to be a rational for the size of the tax, not just punish users.

Of course, taxes are not popular. A tax that did nothing but raise the price of gas to $4/gal from current market price of ~$1.50/gal would not really do 'nothing' else. There would be a general revolt of the populace. With a plausible plan to transition to something else - maybe, just maybe a tax would be accepted. After all, we have been willing to pay a gas tax that is dedicated to road building and repair. I maintain that it was the link to a specific use that has made that tax somewhat OK.

A tax that did nothing but raise the price of gas to $4/gal from current market price of ~$1.50/gal would not really do 'nothing' else. There would be a general revolt of the populace.

Would there?  PR (unfortunately) is everything, and if the tax was (a) sold as a measure against the Islamic Republics and Venezuela and (b) rebated to the public as a tax credit, voters would probably go for it; I know I would.  Hummers and Excursions and Durangos are not all that popular right now, and anything that helps Detroit sell hybrids and PHEVs instead of SUVs can be sold as a bridge to the future.