About 1.4 million immigrants are needed per year, through 2050, to maintain a constant number of working age population in the U.S.

From United Nations population study: unpd-egm_200010_un_2001_replacementmigration.pdf
Major findings of this study include:
• During the first half of the 21st century, the populations of most developed countries are projected
to become smaller and older as a result of below-replacement fertility and increased longevity.
• In the absence of migration, the declines in population size will be even greater than those
projected and population ageing will be more rapid.
• Although fertility may rebound in the coming decades, few believe that fertility in most
developed countries will recover sufficiently to reach replacement level in the foreseeable future,
thus, making population decline inevitable in the absence of replacement migration.
• The projected population decline and population ageing will have profound and far-reaching
consequences, forcing Governments to reassess many established economic, social and political
policies and programmes, including those relating to international migration.
• For France, United Kingdom, the United States and the European Union, the numbers of migrants
needed to offset population decline are less than or comparable to recent past experience. While
this is also the case for Germany and the Russian Federation, the migration flows in the 1990s
were relatively large due to reunification and dissolution, respectively.
• For Italy, Japan, the Republic of Korea and Europe, a level of immigration much higher than
experience in the recent past would be needed to offset population decline.
• The numbers of migrants needed to offset declines in the working-age population are
significantly larger than those needed to offset total population decline. Whether those larger
numbers of migrants are within the realm of options open to Governments depends to a great
extent on the social, economic and political circumstances of the particular country or region.
• If retirement ages remain essentially where they are today, increasing the size of the working-age
population through international migration is the only option in the short to medium term to
reduce declines in the potential support ratio.
• The levels of migration needed to offset population ageing (i.e., maintain potential support ratios)
are extremely large, and in all cases entail vastly more immigration than occurred in the past.