I'm horribly offended you would say such a thing to someone directly. It's not your body, it's not your business, and it's silly to assume she hasn't already considered something like this.
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...).
I'd sincerely suggest you reconsider looking into adjusting the quality of life in countries where high birth rate is actually a problem before telling someone how many babies they should or shouldn't have in a country with a fertility rate below replacement levels.
The USA is not a closed system. If Americans want a lot of kids, the most ethical choice is to adopt many of them from overseas.