We have been at elevated levels for decades since then and now admit about 1 million a year. The proportion of the foreign-born population is set to hit a record in 2025.
This means there is a lot of room to reduce immigration without shutting our doors entirely. Cutting half legal immigration to the levels of the early 1980s would still mean roughly 500,000 new immigrants a year, a high absolute number compared to almost every other country in the world. Of course, the Trump policy that has caused such a reaction is not close to change of this scale.
Trump has also temporarily suspended the US refugee program and capped it at 50,000 refugees. This is in the same ballpark as the figure for admittances from the last five years or so, when the number of refugees was typically between 50,000-70,000 a year.
If we are using an overall level of refugees to judge our American-ness, 1976, 1977, 1978, 2002, 2003, 2006 and 2007 must have been woefully un-American years because the number of refugees was less than 50,000 in each of them.