I am puzzled by the way that some people here seem to assume that if JFK didn't become president, one of his brothers would have. JFK's own path to the presidency was full of contingencies and close calls, and it hardly follows that because he ultimately became president in OTL, Joe, Jr. (had he survived) or Bobby would have in 1960. The brothers were not clones, and each had his own strengths and weaknesses.
On Joe, Jr., I'll repeat an old post of mine:
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The late William G. Carleton, a University of Florida historian and political scientist (and occasional speechwriter for Joseph Kennedy, Sr.) expressed some doubt that Joe, Jr. would ever have become president: "If Joe, Jr. had lived, John would not have gone into politics at all. This is not to say that Joe, Jr. would have 'made the grade' in high politics, as believers in the Kennedy magic now assume. Joe, Jr. was an extrovert; he was obviously the politcal 'type'. John's mind was more penetrating and dispassionate, and he did not fit the stereotype of the politician, particularly the Irish politician. What endeared John to the status-seeking minorities was that he appeared more the scion of an old aristocratic Yankee family than the authentic scions themselves. Had Joe, Jr. lived, the Kennedy family in all probability would never have had a President at all. (In part, this evaluation of Joe, Jr. and John is derived from personal observation. I recall vividly an evening, April 4, 1941, when I was a guest at the Kennedy home in Palm Beach. Following dinner, the entire family, including the younger children, assembled in the drawing-room for a discussion of public affairs...Mr. Kennedy, John, and I were the chief participants, although Mrs. Kennedy and Joe, Jr. often broke in with comments. It was clear to me that John had a far better historical and political mind than his father or his elder brother; indeed, that John's capacity for seeing current events in historical perspective and projecting historical trends into the future was unusual..."
https://books.google.com/books?id=nrFlAgAAQBAJ&pg=PA203
The fact that Jack was more bookish (no doubt illness gave him more time to read) and Joe, Jr. more extroverted and closer to the stereotype of the Irish politician may explain why Jack appealed more than Joe, Jr. ever could to intellectuals like Carleton, but it hardly proves that Joe would have been less attractive to the electorate as a whole. I think one reason for Carleton's admiration for Jack is that Jack, unlike Joe, Jr., was edging away from his father's isolationism at an early stage. Yet Joe, Jr., too might eventually have disassociated himself from some of his father's more controversial positions had he lived. Joe, Jr. might have been tempted, for example, if he were elected to the Senate, to oppose the censure of Joe McCarthy (a hero both to his father and to many of his Boston Irish constituents) but he would have to realize that this would wreck his chance of getting the Democratic presidential nomination. (Jack of course managed to avoid the vote due to back surgery, an option which presumably would not be available to Joe...) If Robert F. Kennedy could morph from a McCarthy aide to a liberal Senator from New York, one should not assume Joe, Jr. would always retain his America-First politics of the early 1940's.
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I would add to this that even if one assumes that Joe, Jr. would be ideologically acceptable to Democrats in 1960, it doesn't necessarily follow that he would have won the presidency. JFK once remarked that Joe, unlike him, would have succeeded in becoming Stevenson's running mate in 1956. But then, JFK added, Ike-Nixon would have overwhelmingly defeated Stevenson-Kennedy--"And today Joe's political career would be in shambles..."
http://books.google.com/books?id=nsOlkJ7yVhMC&pg=PA182
Instead of assuming that some Kennedy, any Kennedy, was bound to win in 1960, we should look at other alternatives like Adlai Stevenson (if the Democrats could nominate Bryan a third time, we can't rule out that they would do the same with Adlai), Lyndon Johnson, Stuart Symington, or maybe even the man who came very close to winning in 1960 in OTL--Richard Nixon...