A carbon tax will not achieve the goal of substantially mitigating global climate change.
There is one, and only one, reason for instituting a carbon tax: to attempt to mitigate the impacts of climate change induced by humankind's use of fossil fuels for the production of energy. And about the only thing that a carbon tax in the United States will not do is mitigate global climate change in any meaningful—scientifically, or otherwise—manner.
Why? Because, based on mainstream estimates, of the approximately 3°C of global warming that is being projected to occur between now and the end of the century as a result of anthropogenic carbon (dioxide) emissions, the U.S. contribution will only be about 0.2°C, or about 7 percent of the total warming. And this is assuming that no carbon tax is put in place. Carbon dioxide emissions from the rest of the world—primarily driven by rapid emissions growth in developing countries like China and India—will be responsible for the other 93 percent of temperature rise.
The best that any carbon tax in the United States could ever hope to achieve would be to reduce the amount of global warming across the 21st century from about 3.0°C down to about 2.8°C. And that tiny, inconsequential reduction would only occur if all greenhouse gas emissions from the United States were halted forever, starting tomorrow, which isn't the plan.
The emissions reductions under any sort of carbon tax will be realized slowly, reducing the magnitude of the global temperature rise that the tax would avert. For example, a carbon tax designed to smoothly reduce our greenhouse gas emissions from their current level to zero by the year 2100 would result in only about 0.1°C of global temperature "savings"—an amount, on its own, not worth pursuing.
Any perceived utility of a carbon tax does not lie in domestic reductions, but in the hope that it will spur technological innovations for cheap, reliable, nondangerous, environmentally friendly, zero-emissions energy production which would then be freely shared with, and quickly adopted by, the rest of the world. That seems wishful thinking on the time scales that matter.