Much of conservative/libertarian America holds up as its ideal a sort of John Galt type of independent entrepreneur. If left free of government interference, the open market will reward smart, hardworking people with wealth and security. In this worldview, every negative thing that happens is the result of politics and the government, and Washington is the only thing standing between themselves and their own personal prosperity.
For people with this mindset, voting for the Tea Party is not against their self-interest, as they view themselves as future members of the 1% if only bureaucrats would get out of their way. Self-interest has not been abandoned by the Tea Party; the identity of Tea Partiers is inextricably linked with self-interest. Tea Party -> Laissez-Faire Capitalism -> Self-interest.
A carbon tax utilizes the Right's fetish for property rights to drive home an environmental message. When I pollute, I damage your standard of living by making you breath noxious fumes and make your kid more likely to have asthma. You deserve to be compensated for that damage, just as you would deserve compensation if I wrecked your car or took your lunch money.