From "Laugh and Be Happy" by Randy Newman:
"Now the country that we're living in
You mean the good ol' USA?
That's right!
It's never been about keeping you out
It's about inviting you in and letting you play"
Used to be we weren't too afraid of the folks walking off the boat. Heck, there weren't any real limits on who entered the country until WWI. Before 1894 you just walked off the boat and went to find work. There weren't any immigration officers then.