Alexandria Ocasio-Cortez has taken a lot of twitting from the right over her recent performance on “The Daily Show,” when host Trevor Noah interviewed the left-wing political neophyte likely to become a Democratic member of Congress from New York. After Noah asked how she was planning to pay for her platform, which includes Medicare for All, a jobs guarantee and free college, Ocasio-Cortez offered the comparatively paltry revenue that could be raised by upping taxes on the wealthy and suggested that a carbon tax could pick up most of the rest of the tab.

“If we implement a carbon tax,” Ocasio-Cortez said, “that’s an additional amount . . . of . . .  of . . .  a large amount of revenue that we can have.” She also wildly misstated the military budget. Conservative went to town.

To some extent, episodes like that are to be expected: Ocasio-Cortez is the latest fad in progressive politics and her political opponents are going to try to knock her down a peg, or eight. Even if she isn’t fluent yet in Bland, the evasive lingua franca of Washington, she is hardly alone on the left in longing to fund favored policies by taxing carbon, mostly in the form of industrial emissions. But how large would that “large amount of revenue” actually be?

The obvious answer: as big as you want, with a big-enough tax. Consider one of Ocasio-Cortez’s proposals for which the projected costs are known: Medicare for All. According to both the right-leaning Mercatus Center and the left-leaning Urban Institute, Medicare for All would cost about $32 trillion over 10 years. Meanwhile, according to the Environmental Protection Agency, the United States emitted an average of 5.4 billion metric tons of carbon over the three most recent years for which data is available. Using the highly scientific method of mindless trend extrapolation, we get roughly 54 billion metric tons over a decade. To cover that $32 trillion Medicare for All bill, a tax of $592 per metric ton of carbon would be required.

Note the assumption that jacking up the price of carbon to nearly $600 a metric ton will have no impact on the amount of carbon emitted. That assumption is . . . heroic. In 2013, the Congressional Budget Office estimated that a carbon tax of a mere $20 a ton would lower carbon emissions by about 8 percent. We can probably assume that a tax 30 times that size would prompt a significant reduction in emissions.

Which is good! But with every 1 percent decline in carbon use, the tax must be raised by a little more than 1 percent to compensate. If carbon emissions declined by 25 percent, to roughly 40 billion metric tons a decade, hiking the tax to $800 per metric ton would be needed to hit the $32 trillion target.

But the CBO notes that even the comparatively modest carbon tax it envisioned would likely have some deleterious effects on economic output, and employment and corporate profits, which is to say all the other stuff we’re already taxing to fund the spending we’re already doing:

A really large carbon tax would presumably have really large effects, making it even harder to reach the Medicare for All target.

But let’s stick with the unrealistic assumption for the moment and move on to the question of what effect the carbon tax would have on ordinary folks and thus what hope it has politically.

According to the CBO, a $20 carbon tax would raise gas prices by about 20 cents a gallon. Assuming this scales linearly, the $600 tax envisioned above would raise gas prices by about $6 a gallon. With the average driver using about 650 gallons of gasoline a year, that’s a budget cost of almost $4,000 a year per driver.

And that’s just automotive consumption; it doesn’t count air travel, electricity, steel production and so forth. Those numbers are harder to calculate, but they all add up to one thing: Funding Medicare for All mostly or entirely with a carbon tax would put a severe crimp in many household budgets. People with low incomes, especially in rural areas, would be hit especially hard.

Advocating for a regressive tax that would hammer the poor is probably not the best look for a proud socialist like Ocasio-Cortez.

I’m not opposed to some sort of carbon tax. I would rather not take risky bets with the only climate we have, and taxing carbon is a good way to lower the stakes. But political realities mean that any carbon tax is likely to be rather dainty. The revenue would almost certainly be dedicated to tax relief for the people the tax would hurt, not to a festival of new spending. As Ocasio-Cortez will learn, if she is elected in the fall as expected, sincerity and principles in Washington are rarely any match for angry voters waving their pocketbooks.