If nature is any guide, extreme population explosions are always followed by die-offs. Lemmings and certain rat populations periodically breed to enormous levels and then run out of food and croak in large numbers.
As far as I know, our species is the first to actually predict that we're going to run out of a necessary resource (in our case, it may be water or air as likely as food) and to consider doing something about it. But I think you and a handful of others are in the vanguard, and most of our seven billion fellows are only dimly aware of the problem, if at all.
The snag is that even you pioneers are late to the party. Even if we stopped breeding today, it would still take many decades to bring the population down to a sustainable level, and there's no guarantee that the environmental damage we've done can be reversed in that amount of time.
And, of course, we won't stop breeding today. Or tomorrow. And the resources necessary for human life will continue to be depleted.
Unless there's a miracle, my guess is that we will not reduce our numbers in a planned fashion, nor will we be able and willing to restrict our resource consumption in time to prevent Mother Nature from stepping in and taking care of it for us.
Naturally, I'd love to be proven wrong.