We already collect federal excise tax on fuel. Changing the amount has a trivial cost. We already collect withholding tax from individuals. Changing the amount has a trivial cost (your boss adds money to your paycheck every week instead of removing it if your tax rate is now negative, retirees and people on disability/unemployment have the amount added to their existing social security/benefits check).

There would be a minor one-time cost for the small minority people none of that applies to, to fill out a form specifying where you want the money to be deposited or the check mailed. But the fundamental process of distributing the money would be a transfer of a fixed amount to each citizen with a social security number, which is easily computerized.

This misses embodied carbon in imports and much of the emissions from domestic agricultural and industrial processes, which are surely large enough to not be ignorable.

If you want to only tax fuels, that's a start.

Obviously the administrative cost of taxing some other emissions source is going to depend on the nature of that emissions source, but if hypothetically evaluating emissions from certain sources turned out to be prohibitively burdensome, that would not be any excuse to avoid doing it for fuels at a minimum, which constitute the majority of emissions anyway.

And a more efficient way to handle imports would be to impose general tariffs on imports from countries that don't themselves impose a carbon tax, rather than trying to calculate the effects of something happening in a foreign country. Which would have a more significant effect anyway, because causing the entire country to reduce its own emissions would be a much bigger win than causing only their exports to do so.

The cost would probably be similar to the COVID stimulus. Maybe they can require the dividend to be distributed using FedNow to drive down the cost somewhat.