People have been talking about over-population for decades. This falls into the same doomsday syndrome category as global warming and all other types of apocalyptic predictions.
Paul Ehrlich wrote a book called
The Population Bomb about this same topic in 1968. In the book, he preaches doom and gloom as he predicts that by the 1980s there will be massive famine that will wipe out a significant portion of the population.
Yet he failed to take into account the impact that technological advances would have on his doomsday theories. Most notably, he did not know (nor could he have known) that something called the "Green Revolution" would shortly revolutionize the agriculture industry, thus increasing the output of farms by many times. The Green Revolution was basically when modern agriculture began. Through the use of capital-intensive methods such as selective breeding, genetic engineering, advanced irrigation and fertilizers, mankind was more than able to feed the expanding population and still is today.
The dangers of population are not inherently in growth or an "explosion". The dangers are in the age distribution of the population, or the "peaks and troughs" of a population distribution graph, if you will. This is especially true for social welfare programs like social security. Here is a graph to show what I mean by the peaks and troughs.
Although the US graph is slightly different than other first world countries, they are quite similar. A third world country's graph looks much different, with more of a triangle shape to it (because they have a lot of kids and many die young).