Of all the alternatives to JFK or LBJ, Symington--"everyone's second choice"--probably had the best chance to get the nomination. To quote an old soc.history.what-if post of mine:
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According to Theodore Sorensen's *Kennedy*, p. 145, "Privately, he [JFK]
thought that Symington, had he organized earlier, might have been able to
defeat him among the more conservative Democrats of Indiana or Nebraska;
and one defeat would have been enough to deny Kennedy the nomination."
(Remember, LBJ at this time was officially not a candidate and said that
his duties as Majority Leader precluded campaigning, so Symington would
have no active competition among relatively-conservative Protestant
Democrats had he campaigned.) But Symington wanted to avoid any risk of
pre-convention defeat (I guess he figured that if he didn't campaign--and
indeed officially denied he was a candidate, though allowing his name to
be placed on the ballot--his doing poorly in the primaries wouldn't be
considered a defeat, whereas if somehow he would do well in any of them,
this would be considered noteworthy)--which of course was itself a risky
strategy since it hazarded everything on there being a convention
deadlock.
All the same, I can't say that there was no chance the strategy would have
worked. Just because time after time the oft-predicted brokered
conventions have failed to emerge in the twentieth century doesn't mean
they never could have done so, and this had a better chance of happening
in 1960 than in later years, when primaries became more important. In
spite of all JFK's primary victories, his nomination on the first ballot
was a close thing. See my discussion at
http://groups.google.com/group/soc.history.what-if/msg/1f78cee90165d362
about how it might have been prevented if Iowa had been required by the
convention Parliamentarian to vote for its favorite son (Governor Herschel
Loveless) on the first ballot. And *if* JFK had fallen short on the second
ballot as well, anything could happen...
https://groups.google.com/d/msg/soc.history.what-if/NfgAk5LUW4Q/_jb658pTYI8J