Not following the complaint that a carbon tax would drive some companies out of business. So what? Right now, those companies only survive because they can pollute and cause millions (billions?) of health damage to the US population and not have to pay for it. A carbon tax attempts to make those companies account for the cost they currently dump on others. If they can't afford it, they should go out of business. And it's ridiculous to say that we suddenly will be without power. If power supply drops and becomes scarce, remaining power will be in demand and the price for power will increase, which will be enough to keep power companies in business as long as they can break even (or make a small profit) at the marginal power price point. It's a market-based solution, which appeals to people in both parties.
It's not quite an ideal distribution of the tax monies received, as the benefits of the tax go to everyone, as opposed to just those harmed by the pollution in proportion to the harm they receive, but it's a good effort anyway. However, the legal system is probably worse, as the lawyers end up with a healthy chunk of those funds so the damaged parties get less than their fair share that way too. The legal system gives a more proportional distribution to those harmed, but skims a large amount off the top for providing this proportionality. A tax system gives back more, but many people who were never harmed receive benefits. Since pollution affects a large portion of the populace, though, the tax system may be the better approach to the problem.
The part I disagree with about the plan, if I'm understanding it correctly, is giving polluters immunity from lawsuits for carbon pollution. I'm ok with this going forward (effectively the tax is a lawsuit settlement they are paying in advance), but people should still be able to sue for pollution harm that occurred before the tax goes into effect. There is no reason why polluting power companies should get away with profiting at the expense of harm to others in the past - they should be held to account for that. Hopefully this is how the plan will work, although I'm pretty sure immunity from past suit is exactly what power companies are asking for in exchange for agreeing to a carbon tax (as if they are entitled to get away with earlier theft).
As an analogy, imagine a shoplifter was coming to your store daily and stealing some of your merchandise each day. One day, you say, this has to end, and you somehow manage to automatically charge him for anything he takes going forward (and he actually pays). That should not give shoplifter immunity for you suing for the value of everything he took in the past.