John Calvin Coolidge, Jr., served under President Harding. He was the only VP or president to be born on July 4th, although three died on that date. Coolidge was not favored to run for VP, but here is how it happened according to Wikipedia:
"At the1920 Republican National Convention most of the delegates were selected by state party conventions, not primaries. As such, the field was divided among many local favorites. Coolidge was one such candidate, and while he placed as high as sixth in the voting, the powerful party bosses never considered him a serious candidate. After ten ballots, the delegates settled on Senator Warren Harding of Ohio as their nominee for President. When the time came to select a Vice Presidential nominee, the party bosses had also made a decision on who they would nominate: Senator Irvine Lenroot of Wisconsin. A delegate from Oregon, Have Faith in Massachusetts, proposed Coolidge for Vice-President instead. The suggestion caught on quickly, and Coolidge found himself unexpectedly nominated."
"Coolidge often seemed uncomfortable among fashionable Washington society; when asked why he continued to attend so many of their dinner parties, he replied, 'Got to eat somewhere.'"
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