I believe the population is predicted to stabilize at about 10 billion based on population growth trends and many experts opinions. If you think about it then it makes sense, the population wont grow above what is naturally sustainable because without resources it is impossible. Many people believe that human numbers will just keep expanding but that is just not feasible.
You are right that the population can't grow beyond what resources can sustain, but let's think about what "stabilization" means. In the best case scenario it means that the 3rd world population will become more educated and their birthrates will decrease as a result. In the worst case it means that war and disease will savage us.
I think most opinions on this are guesses at best. Population collapse happens, and it's reasonable to think that a sudden shift in climate could bring about enough stresses to make it happen to us. I don't think growth is so much the issue as is instability in the environment. We've been able to adapt to our growth, but I'm not sure we can grow and adapt to other changes at the same time.