If you were on a raft in the amazon river and there were 12 people with you and it was a cloudy day and the current was running the wrong way...
People come up with these hypothetical situations to get veg*ns into a bind about what they would do in a particular situation. Now I realize the situation that you present is a real-life scenario but you have to look at the bigger picture. If people actually valued animals and the environment then we could all live comfortably and eat food that didn't cause so much needless animal suffering. But we value the economy and wealth so that takes precedence over so many other considerations. As Sevenseas points out, we have a lot of problems with the overpopulation of humans and a lot of them are suffering terribly. If we (all people) wanted to remedy the situation we could. We could aim at reducing the human population (ever notice how certain well-off western countries have lower birth rates) and having everyone live with a certain standard of food, shelter and clothing. But we don't so we don't.
So what could we do for alternatives to the situation you presented? Well, we could focus on a long-term solution that would involve giving wildlife the proper habitat space, reintroducing animals that were killed off (by humans) and then fencing off agricultural land so that the wildlife couldn't enter into those areas. To have a drastic reduction in the "need" for agricultural land we would probably have to have people switch to a *gasp* vegan diet. That would also address other problems such as the dire water situation the world is coming to grips with.
But people don't want an animal friendly solution right now. So we will stick with the annual deer torture, um, I mean "harvest". Yes, it's true that not every hunter has perfect aim and a certain percentage of those deer will be hit and will get away to bleed to death. And I'm sure I've read many times here on VB
about how deer will populate themselves to suit the food situation. Less available food = less deer. But I'm not sure how that all works so I'll let someone else explain it.
Basically it comes down to what we value. If we value the earth and the animals we will come up with a solution that takes them into consideration. If we value humans then we will choose not to "harvest" the excess humans.