Yes, carbon emissions are the driving factor of climate warming. Those emissions are driven by "always low prices": not just for carbon, but for all goods and behaviors enabled by cheap carbon.

Taxing carbon will affect most of these things, but after some short transition period, all of them will continue to expand again based on other resources. Global warming is the warning that our basic economic behavior model for civilization (city-based society founded on human colonialism/consumptionism/overpopulation) is backward. A common mistake (not saying yours) is to then jump to "overpopulation" as the problem and ignore the basic behavior of taking instead of giving (colonialism). I cite overpopulation because it's part of our contemporary economic paradigm (cities compete with each other based on growth rates and Capital(ists) encourages overpopulation to reduce Labor costs without paying for the maintenance of excess population).

We step over the consumerism problem to get to the carbon problem. One could argue that it's a "chicken vs egg" issue, but only if you ignore that a chicken was once a dinosaur, and it will eat you if you don't stay on your feet. Unfettered consumerism laid the egg of fossil fuel overconsumption (especially autos and highways/sprawl). It will lay another egg to keep consumption growing (war, deforestation, Moon-mining, fission and fusion plants, weather modification, ocean rapacity, etc). Quantitatively, as a carbon tax reduces carbon use, the tax would have to ramp higher and higher to have the same effect on overall consumerism. If you start right out with a consumption tax on everything, then you don't have to shift it around later (inviting corruption like the present income tax code does).