There would seem to be no reason for the polymer industry to discriminate among feedstocks. Hydrocarbons are hydrocarbons, and any viable source of same will serve our purposes. It is as yet "early days", but with increasing frequency we see hints that the day of the dead dinosaur as the source of our polymers is drawing to a close.
The very basic research is underway, and it's interesting! Brookhaven National Laboratory has released information on recent proof-of-principle experiments conducted by biochemist John Shanklin and his team (and funded by the Department of Energy and Dow Chemical). They re-engineered a common laboratory plant (sort of the botanical equivalent of fruit flies and white mice) to produce commercially interesting concentrations of omega-7 fatty acids.
Without going into detail regarding fatty acids it suffices to say that the molecules in question are long chain hydrocarbons, and the path from them to (at least) polyolefins ought to be just chemical engineering.
Of course, myriad open questions remain with respect to reduction to commercial practice and the implications of diverting arable land from food production to plastic plantations. (Of course, it wasn't that long ago that all of our elastomeric materials (i.e., rubber) came from plantations.) But to me, the take-away here is that the march toward an (inevitable?) shift away from fossil hydrocarbon feedstocks toward botanical feedstocks for polymers has begun. And serious commercial enterprises (like Dow) are working the problem.