The big issue I think with the tax is that its ultimately paid for by consumers and not capital, as a result behavior won't shift, people will just get poorer in need of more subsidy and wealth will be more concentrated. Rather than a carbon tax, we should tax wealth for carbon used to generate such wealth in the American economic system. We could do this by taxing the holdings directly, or having a progressive tax rate that is effectively zero for the sort of purchases a middle class individual will make in their life, and quite steep for the sort of purchases that are more common among the elite with substantially larger carbon footprints.
The degree of tax is just too small right now to realistically expect major impact on behavior.
We'll see what happens as tax continues to ramp.