Early in 1956 there was speculation that Eisenhower would not run for a second term because of concerns about his health. In 1955, Eisenhower had suffered a serious heart attack, and in early 1956 he underwent surgery for ileitis. However, he quickly recovered after both incidents, and after being cleared by his doctors, he decided to run for a second term. Given Eisenhower's enormous popularity, he was re-nominated with no opposition at the 1956 Republican National Convention in San Francisco, California.
The only question among Republicans was whether Vice-President Richard Nixon would again be Eisenhower's running mate. There is some evidence that Eisenhower would have preferred a less controversial running mate, such as Governor Christian Herter of Massachusetts, and according to some historians (such as Stephen E. Ambrose, Eisenhower privately offered Nixon another position in his cabinet, such as Secretary of Defense. However, Harold Stassen was the only Republican to publicly oppose Nixon's re-nomination for Vice-President, and Nixon remained highly popular among the Republican rank-and-file voters. Nixon had also reshaped the vice-presidency, using it as a platform to campaign for Republican state and local candidates across the country, and these candidates came to his defense. In the spring of 1956, Eisenhower publicly announced that Nixon would again be his running mate, and Stassen was forced to second Nixon's nomination at the Republican Convention. Unlike 1952, conservative Republicans (who had supported Robert Taft against Eisenhower in 1952) did not attempt to shape the platform. At the convention, one delegate voted for a fictitious "Joe Smith" for Vice-President to prevent a unanimous vote. (Wikipedia)
Word of the “Joe Smith” vote spread quickly among the very large contingent of Nixon detractors across the country and during the campaign “Go With Joe Smith” cigarettes showed up at party functions. The cigarettes were made by The Tobacco Blending Corporation of Louisville, KY which also made the “I Like Ike” and “Stevenson For President” packs that year. As a footnote, Tobacco Blending additionally made an “I Go Pogo” pack to support the popular and lovable possum from Walt Kelly’s comic strip of the same name who was running an independent campaign for president himself.