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alternatehistory.com
Oliver Stone's TV alternate history series makes the point that this was a real possibility at the Democratic Convention in 1944. Would FDR have still won the election? Almost certainly. Then Wallace becomes President in early 1945. Do we still have Cold War? Do we nuke Japan? Does Dewey win in 1948?
This is probably one of those situations where a small change in history would lead to big differences down the road.