Heck, one of the words the "Aztecs" used to refer to themselves was "Mexica." Since, as everyone knows, the Aztec came from what is now the SW USA (and thus have an eternal right of return to and political control of their ancestral homeland), the president was quite correct historically.
That is incorrect. Provide any reference if you feel otherwise. The Aztec were in the area of we now refer to as Central Mexico.
http://en.wikipedia.org/wiki/Aztec
There have been no Aztec ruins ever discovered in what is now known as the United States.