You can't double prices on Monday and expect people to move to downtown apartments on Tuesday. If high prices are believed to be temporary, behavior will change very little. A gradual climb, with no end in sight, would have been preferable, in that the economy would adjust incrementally. Unfortunately, even a sharp decrease in fossil fuel consumption will only delay global warming, not prevent it. High-income people who consume far more than their share of fossil energy are escaping their debt to residents of Bangladesh and the bayous of Louisiana, who depend on disappearing wetlands for homes and sustenance.
Poor people can spend it where it buy the most.
Then they won't drive to work. If petroleum is expensive, then alcohol should replace some of it in the pump. So far I haven't seen that in the mountains of Virginia, where moonshiners have been distilling corn for centuries.