As countries grow richer birthrates tend to trend downwards, for a variety of reasons. The one country that actually took population growth seriously and tried doing something about it (China) continues to get shit over its policies today (sometimes for good reason). Just providing people in developing countries with access to contraception ignores many of the reasons that people in those countries choose to have large families.
Finally, I've read that UCSD guy's blog, and while I respect his expertise, I can't get over the fact that his analysis often seems to rest upon rather shaky assumptions. For example, one of the blog posts he links to ("Galactic-Scale Energy") argues that exponential growth means that even a modest ~2% growth rate, sustained into the far future, would result in humanity needing to consume ludicrous amounts of energy. The math is sound, but the assumption is that the human population will also continue increasing exponentially (e.g. 1%), meaning that economic output continues to be divided among the current populace at a rate that is not necessarily exponential. However, if population growth really is slowing down (as statistics show [0]), then 2% growth into the far future with a constant or slowly increasing population results in a ludicrous amount of economic output available on a per-capita basis. The author's point is that unchecked growth is a bad thing; I don't think unchecked economic growth is even meaningful in the context of a population that is no longer increasing. Many of his other posts contain similar 'spherical cow' assumptions meant to make his mathematical models more appealing in terms of presenting his overall message.
[0] http://en.wikipedia.org/wiki/File:World_population_growth_ra..., data from US Census Bureau.