Depends on what you use the tax for.
I live in a very low-income Cleveland suburb (per capita income is roughly $20k). If you used the Carbon tax to pay for a much expanded Rapid (the local light rail service), or made the buses come every 15 minutes instead of every 40 or hour, most of my coworkers would probably stop driving their cars so much. They'd still need them for grocery-shopping, days when the kid would not go to fucking sleep so mommy really needs to sleep in, etc. but even if the tax doubles gas prices they'd probably save money if they just used the bus/Rapid three times a week.
BTW, this kind of thinking is one reason conservatives rarely get anywhere in the black community. If you think of a reason that a left-wing policy would hurt the poor (and blacks a) tend to be poor, and b) the ones who aren't tend to be very sympathetic to the poor), but the Congressional Black Caucus strongly supports it; your first reaction should not be "why are those morons voting against their own interest?" It should be "Why would those rational human beings disagree with me abhttp://politics.slashdot.org/story/15/03/17/0025235/politics-is-poisoning-nasas-ability-to-do-science?sbsrc=md#out their own interests?" In this case the reason is a combination of coalition-building the CBC, and the blacks who overwhelmingly support it, thinks a government dominated by white pro-Carbon Tax liberals would be better for it then the alternative), and a very different definition of their own interests (ie: many of them would actually prefer to drive less and bus more).
It's similar to what happens when Liberals ask "What's the matter with Kansas?" The answer turns out to be a combination of a) different priorities (many Kansans prefer a universe where they make slightly less money and abortion is harder to get), and b) different perceptions of their interests (Kansans tend to think of themselves as people who will be ricvh real soon now; or at least as people who only have a middle-class lifestyle because some rich guy can afford to hire them; which means that if you start talking about taxing the rich they get uncomfortable).