Without the 1965 immigration act U.S. population was on a course to permanently level out at a quite sustainable ~230 million level. Immigration levels of recent decades clearly play a roll in suppressing native fertility to below replacement levels. If the problem really was not enough population, it is actually not very difficult to pursue policies that increase native fertility.

Japan is way over-populated. There is a myth that they face some sort of crisis as they deliberately pursue policies that bring population to sustainable levels. This is actually mostly immigration lobbyists in the west shrieking. Japan is being sensible and will be fine. Certain elements hate the Japanese example.