You seem to have a mistaken notion that the American standard of living is somehow tied to its population - like there's some kind of magical fountain of wealth in the country which has a limited output, and if you add more people then there's less for everyone.
There is, of course, such a fountain, but it's not magical - it's powered by the very same people who drink from it. That's why the country's wealth keeps growing just as its population does - because the new people don't just take, they also contribute. So long as the society is set up in such a way that most contribute more than they take, it can keep scaling up. Broadly speaking, this set-up is a part of the society's culture.
Immigrants (by which I mean people who come and stay, not temporary labor) are fundamentally different from natural-born citizens in one way only: hey bring the baggage of their culture with them. In some cases, that baggage gets in the way of being productive. But that baggage can be dealt away in the cultural "melting pot", so long as immigrants are truly assimilated (instead of being shoved into ghettos), which is generally true of America - in fact, it is a model "melting pot", with anyone who is willing to undergo assimilation welcome to do so.
Now, the processing capacity of said pot is limited, in that it requires the proportion of new immigrants be significantly smaller than the rest of society, so that the latter majority can assimilate them in a reasonable amount of time. But this is a limitation on throughput, not on the total capacity.