According to Theodore Sorensen's *Kennedy*, p. 128, "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 past several decades doesnot mean they never could have done so, and this had a better chance of happening in 1960 than in later years, when primaries became even more important than they were in 1960. 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...
Still, Symington would face a serious problem with the Catholic vote. A lot of Catholic voters would come to the conclusion that JFK had been rejected by the convention solely because he was Catholic--this would seem to them the only plausible explanation, given JFK's victories in the primaries. Symington would almost have to choose a Catholic as runing mate--preferably JFK but he may not be willing to accept. (BTW, *Nixon* might choose a Catholic runing mate if the Demcorats nominate Sumington or LBJ.) The South is less of a problem--true, Symington was pro-civil rights but he was not as offensive to the South on that issue as, say, Humphrey would be, and of course he would have the big advantage over JFK in that section of being Protestant.