There are numerous issues with using legal means to cap out a population, not the least of which is the little emperor syndrome, the prevalance of males that results within the population, and probably the worst issue, the age imbalance.
I agree that major crises will occur as a result of population overgrowth, but those issues are solvable by changing industrial standards. Probably the biggest issue I can think of is the impending water crisis, an issue that isn't caused directly by population growth, but rather by increased industrial usage of water. After that is the unemployment crisis, which may just be a result of modern medicine and long-term peace. The fact of the matter is, the youth unemployment is more significant than the overall unemployment - areas with high youth unemployment see a lot of violence and crime spikes, and traditionally, it has been kept in check by military activity. Egypt, I believe, had a youth unemployment rate of 30% during their revolution. What is this action of restricting birth going to do about that? Those 20 year olds will still be out of jobs when they grow up, thanks to the retirement age rising.
As someone suggested much earlier, womens rights are a better solution. The fact of the matter is, once a woman reaches her 2nd kid, she is considered done in the corporate world. She can keep her job and work normal hours, sure, but she will lose out on a lot of opportunities for promotion. The women who do have 2 or more kids and keep rising in the corporate world? Their kids know their nannies better than they know their mother. As a result, women simply have either no kids or one kid - the social dynamic of having one kid as opposed to two or more is complex, but suffice to say, having one is a lot more manageable than having two. America has culled its population very naturally in this manner since the 1970s. Contrast this to places where women are stay-at-home-mothers, and you can understand why opening prospects for women and merely giving them the chance to reach the top is a very effective way of controlling population.
At the very least, it's better than restricting our right to maintain large families.