That's an interesting what-if because it would no doubt affect the way the Korean War, which started in June 1950, played out. Alben Barkley would have become President and would have quickly had to deal with MacArthur on the questions of whether or not to expand the war into China and whether to use nuclear weapons. Truman dealt with it by relieving MacArthur; whether Barkley would have done that is unclear, but as a new, untested President, it would have been harder, particularly since the advice Truman got from Marshall and Bradley was not to fire him; it was Acheson who pressed for relieving him. If Barkley acquiesced to MacArthur's plans, the end result could be a real fiasco -- a broad war with China involving nuclear weapons that perhaps drags the Soviets into it, possibly resulting in another World War, this time with nuclear weapons.
Barkley would probably have been a one-term President; he was 73 in November 1950. So, whether Korea turned into a disaster or not, it is quite possible that Eisenhower gets elected in 1952 regardless.