Would a Smathers VP really cost JFK that much in the North ? Generally the VP seems to have a really small impact on voters and in JFK's case no one could have expected that his VP would be so important. The man was young and as far as the public was concerned healthy.
Wouldn't Smathers be seen as ultimately inconsequential by black and liberal voters?
I think you have to remember that JFK was already viewed with suspicion by some liberals, who would have preferred Stevenson or Humphrey and who (this is related to their suspicions of JFK's father [1]) remembered JFK's failure to vote on the censure of Joe McCarthy [2], and by some African Americans (who remembered his vote for the jury trial amendment which weakened the 1957 Civil Rights Act). Taking Smathers, who was to the right of LBJ--and who had defeated Claude Pepper in 1950 in a race comparable in its red-baiting to Nixon vs. Helen Gahagan Douglas--would exacerbate these suspicions. (Remember that Nixon seemed more pro-civil-rights than JFK, and that even Martin Luther King, Sr. had favored Nixon until his son's arrest. Even after the phone call, Nixon got a respectable 32 percent of the African American vote--not quite as good as Eisenhower's 39 percent in 1956 but much better than any Republican presidential candidate would in future elections.
https://www.factcheck.org/2008/04/blacks-and-the-democratic-party/ In 1960 the Democrats definitely could not take the African American vote for granted.)
Anyway, even if most of the liberals and African Americans who voted for JFK-LBJ would vote for JFK-Smathers, "most" isn't enough. JFK carried Illinois by 0.19 percent, Missouri by 0.52 percent, and New Jersey by 0.8 percent. If Nixon carried those three states he would have won (not even to mention Michigan and Pennsylvania, which JFK carried by a bit over 2 percent, and which had large black populations--or Minnesota, where JFK won by 1.43 percent, and where some Humphrey liberals were still not happy about JFK's defeating their hero). Very small defections would give those states to Nixon--who would thereby win the Electoral College. And the choice of Smathers would hurt JFK with Stevenson-loving Californians (in the end JFK narrowly lost California anyway but of course he could not know in advance that he would do so, or that he would not need California.)
There is also the obvious fact that seems to be ignored here that LBJ, Symington, Scoop Jackson, Humphrey and the other people mentioned for the vice-presidency were all men of stature, men who could be taken seriously as president--as could Henry Cabot Lodge on the Republican side. One reason that Smathers was never seriously mentioned is that he was an obvious lightweight who could not be taken seriously as president. That might not have changed many votes, but in as close a race as 1960 not that many votes had to be changed. Nixon's claim that JFK was a frivolous immature playboy--in contrast to the more "mature" Nixon--would only be strengthened by choosing someone solely because he was a personal friend.
And above all, what in the world would JFK
gain to counter all these downsides? Florida was still a relatively small southern state in those days, with only ten electoral votes--and it is by no means clear that Smathers would be enough to erase Nixon's 3.03 point lead there. In the Deep South, Nixon was not really competitive except in SC; the only real race was between JFK Democrats and unpledged-electors Democrats (the unpledged electors ultimately voted for Harry Byrd). For the Upper South, someone like Gore would be a safer choice.
Smathers was a pal, no doubt. But Bebe Rebozo, another Floridian, was Nixon's pal (actually it was Smathers who got them acquainted!) and I doubt that Nixon ever considered him as a running mate.
[1] "It's not the Pope who worries me, it's the Pop."--Harry Truman
[2] Yes, he was in the hospital for a back operation but he could have paired if he wanted to.