WI:Ike Vs. JFK in 1960?

Lets say that their is no 22nd amendment that would prevent Presidents from being elected to more than two terms. As a result, Dwight Eisenhower can run for a third term for office in 1960, although if his health would have been a problem would have been up for debate.But lets say that Eisenhower makes the choice to run for President, and gets the Republican nomination.

Lets also say that JFK decides to still run for the Presidency that year and also gets the nomination.

Would Nixon still stay on as VP?

Would LBJ still be in the VP spot?

How would tha race have gone down?Who would have run?

What happens in the short-term?The long-term?
 
The butterflies would be enormous, and it's rather easy for HHH or Symington (LBJ can't win the nomination because he's a Southerner) to beat Kennedy for the nomination. I don't think Kennedy would run against Ike, because he'd lose, badly. In 1956 losing the VP slot was the best thing that could've happened: he was clearly next-in-line for the 1960 nomination after making his national debut (rather like Obama in 2004) without having the defeat being blamed on his Catholicism. Of course that explanation would be a truckload of bullshit, because no one except Christ himself or possibly Zombie FDR could beat Ike, who was essentially an "Independent" President, both by policy and personal views.
 
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