Mother nature has a way of controlling population. problem is we are not satisfied to living to our 70's
We want water and air that is more pristine than it was originally
We want medicine and health care that costs a ton
We want cars that can withstand any accident
The list goes on and on. I think there is a reason that things like aids and the plague happen. It is a way of thinning the herd. If we are going to keep extending live expectancies than at some point we are going to end up having another massive plague type event or we better find a way to control growth.
Controlling the growth is out the question though. Aside from the ethical side of it you create problems among your population where you end up with more of one sex than another. If it goes on for an extended period of time then it also effects the way new generations think as well. China is having some negative effects from their program.
As it is, it seems that nature has it's own way of dealing with this even within humans. You can see where certain civilizations die off or dwindle because they fall below the 2.1 replacement rate. I've seen reports that suggest that if the replacement rates fall below 1.5 (I think is the number) that the situation is irreversible.