The strategy of relying on expansive growth to support the social net is easy, but ultimately unsustainable (not that I have better ideas though).
Naturally overpopulation is controlled by famines and diseases, technology just moves the mark, it doesn't eliminate it yet (there are still famines around). So everything will work out in the end, but it might be rather unpleasant.
Your comment makes talking about population control feel like a taboo (I'm not sure, is it normally considered as such?), and at first one might oppose it on the same principle one would oppose regular bigotry-of-the-day (homophobia, xenophobia and what have you). I think it should be treated instead akin to telling people they can't just dump industrial waste into a river even if the river is on their own property (for a lack of better example...).