What on earth are you thinking about?
Of course, once the population (under your open borders plan) reaches the saturation level (and we are indestinguishable from India or China) people will stop coming. There will no place for them to work... eat... sleep. Just like India, China and parts of Africa due to overcrowding.
In my mind Liberalism is the same thing as socialism which advocates open borders. Just like you are.
Or, somewhat abstractly, when there is no place for them as when the price of rent has risen so high or there is no place for them to stay....
That's pretty abstract, all right. In fact, it defies logic. Why would the rents be so high? What about owning a home? Won't these hordes under your utopian world all have housing? Or, do you advocate their living on the street just so you can have a cheap maid?
China and India etc... are not 'overcrowded'. People are fleeing those places because of the economic conditions there brought about by corruption/socialism/liberalism. If China and India had strong economic growth, people would begin to move TO those areas. There are deserts and Mountain in both of those countries that are unpopulated. Here in Las Vegas, where I live, the desert is being replaced by a city. What is the difference?
The rents would be high because immigration boosts land prices (enriching American citizens that hold that land - again, benefiting us). I was hypothesizing that a crowded and prosperous future America would be so rich and prosperous that the value of real-estate would be so high that the price might begin to disuade some from coming, although wages might also rise accordingly. Probably shouldn't have brought this into the discussion as it isn't too relevant and a bit confusing... lol