I agree with most of your comment except with this comparison:
> Try to imagine a USA where someone from Texas would not be able to move to LA or NYC or the other way around. Border controls against movement on every state-border.
> If you find that hard to imagine try to come up with a really good argument why it should be any different within the EU.
Before the recent migratory crisis free movement of people was not really a very hard pressing issue, even after the inclusion of the former eastern bloc countries.
It only took the currently seen proportion when, as response to the migratory pressure and the reticence of neighboring countries, Germany (unilaterally) signaled that they would accept and welcome the migrants without a clear vetting or logistic process in place.
A more apt analogy would be if NAFTA, originally an economic treaty, evolved into a free movement treaty between the participant countries and then, as the result of some kind of adverse conditions in South America, Canada declared that they were willing to accept the South America migrants that managed to reach their country.
There would be a big migratory pressure on the southern Mexican border (the actual border of that union) and unable to control or unwilling to deal with the problem on its own Mexico started to organize the flow of migrants from its southern border to its northern, passing the problem along to the next country, the United States.
In that hypothetical scenario the parties opposed to the original conversion of NAFTA from an economic treaty to a freedom of movement treaty would be bolstered by this unforeseen and unrelated event.
Two notes:
1) nowhere in this analogy I'm making any statement of opinion or passing any judgement about rhe situation depicted
2) comparing NAFTA to the EU is more apt than comparing US to the EU because the states that make the later have a much stronger and older sense of their own national identity than those of the former.