No Nixon had only 219 electoral votes in 1960. Texas had 24 then, and that would have been insufficient to elect Nixon. Nixon would have needed IL and MO as well, both of which were razor-thin.
IL and TX were both rigged for the 1960 election. If you check the election results in Illinois, Kennedy basically had ZERO support outside Crook county. In BOTH instances, the LEGALLY cast votes in those states went to Nixon. Therefore, American citizens voted to elect Nixon and illegal votes put Kennedy in office.
Illinois primarily had ghost votes in Chicago wards, but illegal alien votes have always provided a nice boost to Democrats here as well.