Well, the utter fiasco that was the Second Bay of Pigs and the first use of tactical nuclear weapons in battle doomed the Kennedy presidency and cast a shadow on LBJ. The 1963 publication of the Green File, as revealed by an undisclosed Defense Department aide, won him a Pulitzer Prize and highlighted the intellectual but grossly inexperienced JFK Presidency by highlighting the worst naivete and reckless actions in regards to Cuba and Southeast Asia. The Johnson Administration's unsuccessful attempt to silence The New Republic from publishing led to the celebrated rejection of censorship in United States vs. Lippmann (1964). Voters thus got reminded of two Democratic administrations in a row grossly mishandling Communist wars, while being reminded of the steady leadership provided by Eisenhower. In addition, the resignation of President Kennedy due to being caught in flagrante delicto with Marilyn Monroe led to much sympathy for his wife but none to his crude, bullying successor.
In addition, the Civil Rights Bill failed because it was far too radical; implement changes to voting procedures and Positive Employment (TTLs version of Affirmative Action) later on rather than as centerpieces of the bill, might lead to passage and prestige. Instead, it drove even moderate Southerners en masse to Goldwater, who while being a damn Republican, was at least not a Yankee and believed in the Constitution (i.e. states rights).
Several PODs come to mind:
- Have Kennedy die tragically rather than resigning in disgrace.
- Have Goldwater appear unstable and dangerous in the debates, or pick an unlikable/unstable VP like Curtis LeMay
- Have the Civil Rights Bill focus on either voting rights or public accommodations and have it succeed.
- Have Johnson pick a non-Kennedy successor like Pat Brown of California.
- Avoid the revelation of Pentagon warmongering and Kennedy incompetence.