I realize that some people take for granted that JFK would have dumped LBJ in 1964 but the evidence is mixed at best. See my post at
https://soc.history.what-if.narkive.com/ADTdAkOO/jfk-retires-1964#post8 (my apologies for any links that may no longer work):
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There was a lot of talk in late 1963 that LBJ might not be on the ticket, especially in the wake of the Bobby Baker scandal. Evelyn Lincoln in 1968 claimed to remember a conversation with JFK in November 1963 where he told her that he was thinking of having North Carolina Governor Terry Sanford as his running mate in 1964, but that in any case "it will not be Lyndon."
http://books.google.com/books?id=0xqrU5lnD7AC&pg=PA605 OTOH, Ben Bradlee claims (in *Conversations with Kennedy*) that in an October 22, 1963 conversation, "As for dumping Lyndon Johnson from the ticket in 1964, the president said 'That's preposterous on the face of it. We've got to carry Texas in '64 and maybe Georgia.'"
http://books.google.com/books?id=E5y77o-G2SYC&pg=PA217
It was undoubtedly unrealistic for JFK to think he might carry Georgia in 1964 (maybe he had in mind that it was the only Deep South state to go for Truman rather than Thurmond in 1948) but Texas was another matter. Polls showed a close Kennedy-Goldwater race there, and I can't see JFK writing off such an important state. For that reason, I don't think he would have dumped LBJ unless some scandal made him really a liability. FWIW, when Arthur Schlesinger, Jr. asked RFK about Lincoln's account, RFK supposedly replied not only that there had never been any intention of dumping LBJ, but "Can you imagine the President ever having a talk with Evelyn about a subject like this?" Schlesinger, *Robert Kennedy and His Times,* p. 605.
Also, JFK supposedly told George Smathers that dumping LBJ would be foolish because it would make the Bobby Baker affair look like a really serious scandal--which JFK insisted it wasn't--that would reflect on the president. LBJ himself wrote his brother that he expected to be re-nominated, that while there were some people around JFK who disliked LBJ, the president himself had always been fair to him.
http://books.google.com/books?id=0xqrU5lnD7AC&pg=PA605 (Of course one must note that it was in the interest of RFK in 1968--and of his friends and supporters like Schlesinger--to say there had been no such "dump LBJ" plan in 1963; otherwise, RFK's 1968 campaign against LBJ would look too "personal", too much a "let's dethrone the usurper" campaign, rather than one based on principled differences.)
There is in any event a good reason why despite talk of presidents dumping their vice-presidents in a re-election year, it very rarely happens. Choosing a running mate (yes, technically, the convention does it, but in recent decades the presidential nominee's choice is almost always nominated) is the first and one of the most important decisions a presidential nominee makes. (Although it almost never makes a difference in the election results, since as Steve Chapman points out at
http://www.slate.com/id/84823/ "Nobody Votes for the Veep.") In effect, he is choosing his successor should he be elected and die in office. To admit to a misjudgment on such a serious matter would be a huge political embarrassment--normally a much greater one than retaining the vice-president. (Ford-Rockefeller was an unusual situation, Ford never having been elected president and facing a formidable primary challenge, and Rockefeller in any event not being too enthusiastic about the vice-presidency.)
So all in all, I am not convinced that JFK would have dumped LBJ. The best discussion I know of the issue is by Robert Dallek in *Flawed Giant: Lyndon Johnson and His Times, 1961-1973*, pp. 43-44.
http://books.google.com/books?id=G_J3PEegwdYC&pg=PT58 Dallek thinks that JFK may have had *contingency* plans to replace LBJ if the Bobby Baker scandal got too serious. Moreover, he thinks that JFK's alleged words to Evelyn Lincoln may have been authentic, because on November 20, 1963, JFK was angry with LBJ for not doing anything to "iron out any of the problems in Texas" (presumably referring to the split between the Tory Democrats led by John Connally and LBJ himself versus the liberal Democrats led by Ralph Yarborough). "Kennedy's remarks to Lincoln (if he actually made them) may have been no more than a spontaneous expression of his anger toward LBJ. His larger design, especially once it seemed likely that Johnson would ride out the Baker scandal, was to do the politically necessary thing and keep Johnson in place..."
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I know that since I wrote that post several years ago, Robert Caro has come out in support of the "JFK was going to dump LBJ" position, but I am still skeptical.
(BTW, until some recent research, I hadn't realized that Billy Sol Estes lived until 2013, Bobby Baker until 2017....)