A plastic bag uses very little oil (a quarter teaspoon or so) and some of them can even be made from renewable resources. The real problem is that paper bags are bulky. It takes a lot of energy to move those bags from where they are manufactured to where they are consumed. For the energy cost to get that stack of paper bags to your local grocer you could probably make and transport a hundred plastic bags.
Paper uses more than 4 times as much energy as plastic. And releases much more pollution, and more water, and takes 85 times as much energy to recycle.
