If the population is not stabilized by hunting, nature will step in and thin it with disease and starvation. The enviros will still oppose hunting even when there are thousands of scrawny diseased deer running around spreading who knows what. They will probably want to bring in wolves as a more environmentally friendly method of controlling the herd.
The problem with "starvation" is it'll not happen with one hundred sixty acres of beans and three hundred acres of corn every ten miles or so.