I'd say within 20 years, immigration from Latin America will plummet as fast declining birth rates there keep young people home to work. The same goes for southeast and south-Asia.
The next big immigrant push will likely come from sub-saharan Africa and the Middle East.. the last two regions with high fertility rates. Once those areas see their fertility rates fall (as they certainly will), immigration will slow markedly and the U.S. population will level off and eventually begin a slow fall.
By the time this next (and last) great wave of immigrants reaches its zenith here, how high do you think the population will be in the United States, and what proportion of that population will be composed primarily of first-generation immigrants? For comparison's sake, in 1910 there were around 13.5 million immigrants mostly from southern and eastern Europe out of a total population of over 92 million -roughly 1 out of every 7 Americans was a first-born immigrant.
Do you think we will see something similar within the next few decades?