I've looked around a bit, but only come across "Regan did it" as an answer without much to support it. From what my mother mentioned, immigrants from Mexico had a day of registration every year, and that was it. What changed?
Around Reagan's presidency, drug trafficking was popular. Pablo Escobar and the rest of the Medellín cartel were bringing 15 tons of cocaine to America a day. Many of their trade routes went through the Mexican-American border. This was a big factor to having heavy control over the border during Reagan's War on Drugs.
But even in the past we see that the border has been in constant dispute. The annexation of Texas led to the Mexican-American War, which ended with the Treaty of Guadalupe Hidalgo (1848) where America also gained New Mexico, Arizona, and California. Then the U.S. bought Tucson and Sierra Vista in the Gadsden Purchase in 1854 to build a railway. America gained a lot of land and it's kinda been America's mission to keep it for ourselves, away from the Confederate States during the Civil War, the French, and the Mexicans.