Conceptually, taxing it is very easy. Increasing taxes on fossil fuels will flow down to all fossil fuel derivatives, including plastic. Politically impossible, though.

Just some napkin math, in the US we make 100 billion plastic bags a year out of 12 million barrels of oil. That breaks down to about 200 bags/gallon or .7 cents worth of oil per bag at current oil rates of $57/barrel. If you taxed oil at 10 times the value of the oil, a bag would increase to 7 cents. I'm still not blinking much at that price, it's a rounding error to me and now I have $35/gallon gasoline. It sounds like it's easy conceptually to tax our way out of gasoline, but I still don't think most people would blink at the cost increase to plastic items.

It hasn't helped that people have lumped issues with plastic together with climate change just because they both involve oil. Plastics use relatively little oil compared to transportation, and unless they're burned the carbon isn't released.

Now that you have $35/gallon gasoline, you will have to adjust your whole lifestyle to consume less. 7 cents might start mattering to you now that you are having to make trade offs to meet your budget.