Actually, Lyndon Johnson gets most of the credit for blasting the gate off its hinges.
In the 1950's, he fought Pres. Eisenhower's initiative to reduce Mexican braceros working in the States (during a recession) and tried to keep the floodgates open. Eisenhower went around LBJ, who then was running the Senate, by signing executive orders.
In 1965, just a year in office, LBJ blew up the old immigration quota system completely as one of his principal legislative goals, because he knew that Mexicans vote overwhelmingly Democratic when they get into the voting booth. (The split is about 70-30 overall, among Mexican-Americans.)
You’re about right....I wouldn’t disagree too much with ya there.