How long can the US keep open borders after WWI

The U.S. cut off European immigration in 1924 or so in order to prevent communist agents from infiltrating. However, how long can you keep the US immigration open and how would this effect U.S. immigration and demography if the door is left open for longer. Can it be left open until the Great Depression? Could more Jews be left to flee into the U.S. if it keeps open borders for longer?