Earlier quoted context omitted.
Birth rates are below replacement everywhere in the developed world and China and most other places except the middle east and africa. There is no need for forced sterilization or whatever you were alluding to.
There will be at some point though. Fertility is moderately heritable.
So we'll hit a replacement problem long before natural selection has time to catch up. The replacement issue has already real implications, this will become much more obvious in the course of the next 30 years.
Any relevant change on the population size the propensity for fertility can have; it will take (three, four, five , ...) generations to manifest.