Will plastic run out?

How come with all the scare mongering about oil running out none of the media or politicians seem to be to concerned that plastic and the multitude of other things made from crude are going the way of the dodo also?We can recycle all we want but that will never keep up with the demand.Is this something that is conveniently left out of the picture or am i just to tired and haven't searched properly.

But they could simply dig up all the old refuse tips and get the plastic cant they? After all most of it doesnt degrade

You can make plastic from plant sources and don't have to rely on oil. Sadly, we will not run out of plastic, but I wish we would stop making it anyway.

First, I'm not sure about all, but at least some plastics are said to be able to be made from things other than oil, such as biomass or corn or vegetables.

Second, I'm not sure oil will run out, at least not in the foreseeable future.