EDIT: I made the wikiboxes better
Wikipedia said this
"In 1956, when Eisenhower mulled not running for a second term, he suggested Dewey as his choice as successor, but party leaders made it plain that they would not entrust the nomination to Dewey yet again, and ultimately Eisenhower decided to run for re-election." So I thought, what if Dewey had lost the 1948 nomination (maybe 1944 as well), and the GOP leaders wanted to give the man a chance.
Eisenhower would convince Dewey to run in 1956, and when he did run, the president offered him his full support.
Thomas would win the primaries. He chose Nixon as his running mate, but Tricky Dick would decline (to Dewey's dismay). He would choose Warren instead.
With all of Ike's support, Dewey would win the presidential election.
Dewey would run for reelection.
The Democrats would choose the southern democrat, Lyndon Johnson with the charismatic JFK as his running mate. Though they would argue on policies.
Thomas Dewey would win.
In 1963 Lee Harvey Oswald would shoot Dewey and Warren, with a sniper rifle. Fortunately, the president would survive, but sadly his vice president would die from his wounds the next night.