I'm not sure, but maybe it could be possible with a more anti-union and generally economically conservative Republican than Eisenhower or Nixon being President in the 60s or 70s, with Hoffa and the Unions playing a big role in the opposition. Maybe throw in a painful recession to discredit the conservative economic policy, plus maybe some government investigations into Hoffa that appear politically motivated to help soften the issues with the ties to organized crime (and maybe butterflies can make Hoffa a bit cleaner while still being able to be effectual), and maybe the Democratic establishment at the time is a bit leaning towards the southern an less strongly pro-union elements, and maybe this stuff could be enough to allow an opening for a union leader to make a direct go at the Presidency
 
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