My cousin Dahlia (whose mother, my aunt, is a Mexican immigrant) and I talk about this on occasion. Dahlia is a social worker. Her husband is an immigration attorney.
American problems with illegal immigration go back to 1848. That is when the U.S. decided to expand its border down to what is now Texas and across to the Pacific Ocean. The Mexican government disapproved and the two sides went to war over it.
The U.S. army actually crossed the border and drove the Mexican army out of its capitol. The Mexican government was forced to surrender.
Resisting cries to add Mexico as a part of the U.S., Polk decided to add what is now California, Arizona and New Mexico instead.
It all falls in line with what friends of my brother in law have always told me:
"The U.S. took parts of the Southwest from Mexico in the 1800s. Now we're taking it back."