Honestly, evolution says that it won't. Long-term, breeders will "out-compete" those that limit their household size. Without external political forces or wholesale genetic engineering, we're in for a rough ride.
There are various examples where breeders did not outcompete, and instead a population settled on a low birth rate. Any animal that is not predator-dominated, really, but the best-known examples are New Zealands Kakapo [1] and Panda bears [2].
