There were widespread reports of voter fraud in IL and TX in the 1960 election. If Nixon had won those two states, he would have won the election with 270 Electoral College votes to Kennedy's 252. Kennedy's margin of victory in TX was only 46,000 out of 2.3 million votes cast. Kennedy's margin of victory in IL was even slimmer: 9,000 out of 4.7 million votes cast.
Many Republicans urged Nixon to demand an investigation into the voter-fraud reports and to challenge the results in IL and TX. Even some moderate Republicans were convinced that the fraud allegations were credible enough to warrant a challenge to the results in IL and TX. But Nixon, for various reasons, decided against doing so.
The results in IL were especially suspicious. IL had been a strongly Republican state for the previous two presidential elections. The state went for Ike by 10 points in 1952 and by 19 points in 1956. Similarly, Texas had gone for Ike by comfortable margins in 1952 and 1956. It was well known that Daley and LBJ strongly disliked the Democratic nominee in 1952 and 1956, Adlai Stevenson. The Daley machine in IL and the LBJ machine in TX may very well have given the election to JFK in 1960 because they viewed him as an acceptable Democratic nominee.
Of course, liberal/Democratic authors have always dismissed the idea that JFK owed his victory to election fraud in IL and TX, but this may well have been the case. We will never know because Nixon declined to challenge the results in those two states.
