Many of the people affected will seek some sort of compromise to continue to enjoy and preserve traditional hunting. As gun banning becomes more and more politically correct, the logical response will be to take up the bow and arrow to hunt. Still, on the other side of the coin, there is the argument that any ban on guns will precipitate a ban on hunting in general. I find this too improbable. Plus, if the critters become too numerous, even our own species is at risk.
Nature generally takes care of over-population with disease.
I think the real endangered species today are humans. Long before hunting is banned, I feel the human race is more likely to be brought up short with the results of widespread pandemics, to say nothing of the mess from wars that politics precipitate. That alone will shift the attention of any contemporary political agenda of any special interest group. When we entered the 21st Century, there was all that stuff on the History channel and Discovery. Even Tom Brokaw got into the act with a TV special on the last century.