Abraham Lincoln was the only President I could find who truly owned a large breed "mutt". "Fido" was likely a retriever/shepherd mix.
JFK was no stranger to dogs, and owned a German Shepherd in addition to a slew of others. JFK definitely was the spokesperson for "You can't have just one".
If worsening early Cold War tensions weren't enough, Truman gets his Dishonorable mention here for "Feller", his Cocker Spaniel. Yes, not a large breed, but this is the only thing I've ever read regarding dogs and a President that made me so sad. (Leaving out Presidential hopefuls who let their dogs ride in kennels on the roof of their car). Truman is credited as saying "If you want a friend in Washington, get a dog". Apparently he did *not* want his dog Feller who was given to him, and he surrendered him. Feller would be rehomed several times until finally finding a forever home. He would be sadly referred to as the "Unwanted Dog". Apparently he *did not* want a friend in DC. I know Cockers can be barkers, but Congress barks much worse.