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There is one! My Fellow Americans (1996). 
“Ex-presidents Kramer (Jack Lemmon) and Douglas (James Garner) have hated each other for years. But when the current administration of President Haney (Dan Aykroyd) -- Kramer's former vice president -- tries blaming a string of kickbacks from a defense contractor on the two former presidents, they band together. With Haney's goons trying to kill them, they set out across the country to try and clear their reputations. In the process, they see a side of America they never knew before.”
Reverse National Treasure plot: they all have docs and have to team up to get them back to the Archives. >

I always thought it would be hilarious to put a bunch of former presidents in a anti-buddy-cop movie where they all hate each other but have to team up to save/do something and become best friends along the way.