More on Obama, Pigovian
What I should have made more explicit in my earlier post is that the reason that the relative prices won't change much is that this is a one-time deal. Energy demand shifts slowly, because it mostly requires significant alterations in capital expenditure--insulating your house, downscaling your car, moving closer to work. A one time tax/rebate doesn't give consumers incentive to alter their behavior. Since fuel demand is inelastic in the short term, essentially all you're doing is, on the one hand, raising the price of fuel, and, on the other hand, giving consumers the money, which they will probably spend on fuel. All you've done is wasted a phenomenal amount of energy to produce a very small change in behavior.