How in the world did McGovern manage to pull off such a huge margin of victory in southern Texas?
You say "southern Texas" as though it is "Southern" with a capital S. It is anything but.
South Texas is one of the most partisanly Democratic places in the country. Duval County back then was a fiefdom of the local Democratic machine. In the '40s, their local party chairman helped "nudge" the votes towards LBJ in his Senate primary race.
Basically, poor Mexican farm workers and ranch hands. The sort of place where you used to be able to go into someone's living room and find two pictures hanging on the wall: one of John F. Kennedy and one of whoever the Pope was at the time.