Actually the idea of adding Mexico to the United States was strongly supported by the Democrats in the 19th century. The Whigs objected. Leading problem was that the Mexicans were Catholics, spoke Spanish, used Roman law and were slightly off color.
It also should be noted that Mexico is ALSO very much opposed to open borders, which is why all the Central Americans fleeing incompetent or corrupt governments end up at the US border having passed through Mexico, which was unwilling to grant them refugee status.
The serious advocacy for liberalized immigrations come from employers (who have to be polite about it, since it doesn’t look good to put out a sign “Help wanted – good workers willing to work at low wages”, and those seeking to move to the United States to take the jobs that Americans don’t want (at least, not at the aforementined low wages).