As reported today by the Times, Jeff Passel and D'Vera Cohn wrote a report for the Pew Research Center that revealed a large role for immigration in U.S. population growth to 2050.
The direct effect of immigration on population growth is not particularly large; the flow of new immigrants into the U.S. every year accounts for perhaps one-third of the 1% annual rate of population growth. But new immigrants typically arrive young, with families, and their families tend to be larger than those of the native-born (i.e., immigrants' fertility rates are higher). So Passel and Cohn project immigration will account for 82 percent of the net increase in living U.S. residents, or about 117 million of the 143 million new people we will have by 2050.
This certainly adds perspective. The report also discusses trends in the "dependency" or support ratio --- the number of non-workers per worker. Immigration typically reduces it, meaning that immigrants help pay for Social Security and for kids' education. But the effects of immigration do not appear to be large relative to those of the retirement of the Baby Boom.