Rob, there are 190+ countries in this world to choose from to immigrate to, yet the overwhelming majority keep choosing the U.S. Maybe being the only country in the world that has a "pursuit of happiness" in its constitution has something to do with it?
Desperation... escape... forced departures... banishment. But of course! Almost nobody leaves the country they were born, homes they grew up in, language they speak, their extended families and friends, their memories, graveyards, etc. on a pure selfish whim, or for fun. That's the push factor. But there is always a pull factor, something that attracts you to chose namely the U.S. among those 190+ countries. Nobody (but slaves) was forced to come here, as much as they might have been forced to leave their countries of origin.
You mentioned Jews prior to '39. You will also remember the premise of this debate (i.e., hyphenated Americans). Do you really believe that they will be the ones to declare themselves "German-Americans"!?
As for the "curtains already being drawn"... as much as every country has the right to control immigration, this is still the most immigrant-friendly country, at least that I know of. And not only in their laws and regulations, but in the attitude of the "natives" as well. Immigrants will always have a hard time adjusting quickly and being accepted quickly, most of which is simply human nature, but I never felt this welcome (within reason) in any other country, and believe me, I've been in more than a few.