The story
From the four-year length of an American presidential term. Perhaps popularized by use as a slogan of Richard Nixon's reelection campaign; in 1972, an article in The Guardian on Nixon's victory referenced "the 'four more years' which his supporters have been chanting for all through this election," and the phrase was used as the title of a guerrilla documentary film on the 1972 Republican National Convention. The phrase is attested as early as 1956 in the song "Ike for Four More Years."
Etymology from Wiktionary, CC BY-SA 4.0.