Pinback button promoting William Howard Taft for president, 1908/1912.
The amiable, mild-mannered Taft, elected president with Theodore Roosevelt's blessing in 1908, found himself in a political maelstrom in 1912, due in no small part to Roosevelt, who now wanted the job back. Failing to secure the Republican nomination, Roosevelt bolted the party and ran as a Progressive, taking many Republicans with him. Faced with a revolt within his own ranks, Taft did little to counter the tide rising against him. His own running mate, Vice President Sherman, died a few weeks before the election, an ill omen for an already beleaguered campaign. When the votes were counted, the man left standing was neither Taft nor Roosevelt, but the Democratic dark horse Woodrow Wilson. Adding insult to injury, Taft received only eight votes in the Electoral College. He retired from politics and returned to his preferred branch of government, the judiciary (he was later appointed Chief Justice of the Supreme Court by Wilson).
This button features an actual photo of Taft, and could have circulated in either election.