If no immigration regulations, how big is the US (Pop)

As a point of departure, how about in some early part of the country's history we got a constitutional amendment saying that the US will accept all peaceful immigrants, thus locking in the lack of restrictions if and when anti-immigrant sentiment increases. Not sure when the most plausible period for such an amendment to appear would be, but it seems like the kind of thing that could theoretically happen if there was some brief swing towards intense pro-immigration policies, either to increase the country's population or as a humanitarian gesture.

It would'nt happen since their has never been that kind of Pro-Immigration attitude in the United States, plus their was general opposition to amending the Constitution, I mean after the Original Eleven amendments (which were agreed upon beforehand to be added to the Constitution as amendments) the only amendment prior to 1865 was to simplify the Electoral College after having problems with multiple Presidential elections; it took a Civil War for their to be impetus to pass any real amendments.
 
Top