I might be completely off here, but I imagine these pollution permits are similar to those established by the Kyoto protocol. The idea was that pollution would be "internalised". Except rather than allowing private property to deal with the issue, they instituted an enormous bureaucracy, whereby countries would sell "air" to each other. Essentially, those countries that don't produce anything get money from those that do. Think of it as an elaborate tax. Obviously it also increases costs for producers, who either face bankruptcy (and shortages) or must raise prices. Those that are actually harmed by pollution don't get anything. It's just an elaborate wealth redestribution mechanism from first and second world countries to third world countries.
I think their arguments that private property wouldn't work hinged on stuff like "how do we privatise oceans, lakes, rivers, and the air?". It would be far easier to tackle this issue if we looked at things this way: You don't necessarily own the airspace above your land (how would you homestead it?) but if you are negatively affected by pollution in it, and can trace it back to a particular factory, you can sue them for damages. Same thing with water. You don't need to own a river to be able to sue its polluters if you can prove that you regularly use water from it, that has now suffered due to pollution. This way those that actually suffer get a recompense, and not a corrupt bureaucracy in bed with non-producing countries' governments.
I imagine the EPA does something similar, charging people to allow pollution, except that the government, rather than those that suffer, get the money. I haven't really studied the issue in America though.
"What we do in life, echoes in eternity."