Maybe a new $10/bbl oil tax

You forgot all that fuel oil (diesel, home heating, etc) and other petroleum products? here or the yields.
U.S. Refinery Yield
That's 45% or 18.9 gallons of gasoline + 32.6% fuel oils or 13.7 gallons (diesel has more energy than gasoline so perhaps refiners will add a little more of the tax here) plus other things that can be partially taxed. Lets just take the 32.6 gallons of liquid fuel and tax it equally for the $10 (again gas would be charged a little less in real life) then we get 30.6 cents a gallon, but there are only 0.9 of a gallon of gasoline in a gallon of E10, that makes it 27.6 cents. Why did I say a quarter, or 25 cents. Well I think more would be taxed from the diesel and some from the other components, making it around 25 cents. I really don't know if it will be 20 cents or 31 cents, so I estimated a nice round number. Certainly diesel and home heating oil will get some of the tax, those are prime products. Put the tax high enough and they will crack some of the other components and get a higher yield of liquid fuels.

 

To raise the same amount of revenue yes they would need a higher gasoline only tax.

If you are going reduce dependance on foreign oil then a tax on oil (the thing you want to reduce demand on) then some thought about a $40/bbl tax would add about $1 to gasoline, and $1.20 to a gallon of diesel, but no one knows how the refiners will distribute the tax, and how they would change their product mix. I simply divided by 4 and think this tax will add about $0.25/gallon of gasoline. It definitely could be as high as $0.35/gallon or as little as $0.20/gallon depending on how the refiners allocate the tax.

http://www.economist.com/blogs/freeexchange/2015/07/reducing-carbon-emissions