Happens.
Today, rich industrial and post-industrial states mainly keep up their population by immigration; and I can support the numbers above, even though official government statistics for signapore show 1.2 birthrate in 2011.
Still pitiful.
USA is a special case because of just the thing you said won't matter much in the future: Religion.
It's the only large economy that still contains a statistically relevant amount of people churning out children; whether that's for the better I leave to you.
With a more well rounded social policy, unrests might be limited in the less economically endowed regions, and birthrate might be increased again to self-sustenance, but much higher? not really.
If a world with 5 billions or more has a consistent living standard that on average reaches at least the 80s in central Europe or North America, population will be relatively stagnant even with efforts being undertaken to increase fertility rates.
Short of Religion, political indoctrination or any other given ethos ingrained to the populace, it'll require a significant financial effort.
This gives meaning to politics, however.
A Theocracy could start with less research labs and have have slight disadvantages on other areas, but a higher pop growth in turn.
At least leave it to the SM, that'll allow for nice RP.