The answer to this is for the tax to pay out to everyone as a dividend. Then voters would be in favor because some of the tax is paid by corporations but all of the money goes to individuals, so most people get back more than they pay.

On top of that, the tax would (if enacted by most countries) crush demand for fossil fuels. So then fossil fuel prices go down by, for example, half the amount of the tax, meaning that half the tax get paid by Exxon et al. But all tax money still gets paid out to individuals.