It won't work. Singapore tried to limit its population in the 1970s and all it did was upset the demographics. Graduates stopped having children, less educated parents continued to have large families. Nothing elitist about this, just a simple fact of life.
Taken to an extreme, the movie Idiocracy shows what can happen when people with high IQs defer having families at all while their moron cousins breed like rabbits. After 500 years of opposite growth trends the morons extinguish the brainy ones altogether. A frightening film indeed (even if the ending is, in my opinion, poor, suggesting the screen writers ran out of intelligence).
As to combatting climate change, well, this is one of those government mantras that have been spawned in recent years (probably starting with security after 9/11). For an example of another mantra, read this blog entry on the credit crunch. A pattern emerges.