What you do with that money is irrelevant. Turn it into a big paper boat and float it down the Hudson. The effect is in the levying of the tax, not in what is done with it.
See for example Canada, who directly deposits the revenue back to its residents.
The "augmenting cars" bit comes from people who don't want to pay the (now high) price of fossil fuels anymore, and instead want to avoid that tax by going green. That's how pigovian taxes work. See the UK who introduced a carbon tax, and promptly saw a huge shift in energy production to green energy and lower CO₂ emitting fuels.
This is why many well known economists are for a carbon tax:
Because the will of the people is in the other direction. At this point, its a matter of convincing the greater public of the evidence.
People are stubborn and difficult to convince. And you need to convince roughly half of the voting population (maybe ~50-million people) before things happen in the USA. That's how democracy works.
There's also a power-imbalance that gets somewhat political: how smaller states have 2 senators and therefore control the vote despite having a very small population. Convincing those people is more important, because their vote matters more than most people.
200,000 Wyoming residents have the voting power of 700,000 California residents, due to how Senators work.
Not with gerrymandering, you'll effectively need much more. And then there's the fact that people are consistently voted in on a set of plans/promises that either are never followed through with or they do they opposite because they were just saying the things that get votes rather than what they actually intend to do. The system is broken, plain and simple, and it's not going to change because it benefits those with the ability to change it.
The biggest "problem" is that neither party is predicted to control the House, Senate and Presidency all at once any time soon, so it almost inherently has to be bipartisan. But the prevailing spirit is not exactly cooperation and good faith, on either side.
It’s almost as if the majority disagrees with you that it’s a good idea. Welcome to democracy.
While there is legislative deadlock nothing will happen, and that won't change for at least a year.
Don't give up hope :) keep bringing up carbon price whenever relevant. The tide of public opinion will turn. Late, as always, but it will turn. People didn't think a black man could ever be president but lo and behold you did it. You just need to keep telling people that there is a solution, and that it is carbon price. Keep beating the drum.