Interesting that attitudes haven't changed. I read a bit more about the history of the polio vaccine.
In 1938, FDR founded the March of Dimes, a nonprofit to help people with polio. Incidentally, this is why the US 10 cent coin has FDR's face on it. That nonprofit funded Jonas Salk and Albert Sabin, the researchers who developed two different kinds of Polio vaccines in the 50s. Salk published in 1953, and large scale trials began in '54 and concluded in '55. Note, the Gallup poll was made in 1954, when the vaccine was still in trials. The successful vaccine was then licensed, and promoted by March of Dimes. "The annual number of polio cases fell from 35,000 in 1953 to 5,600 by 1957. By 1961 only 161 cases were recorded in the United States."[1]
In 1955, a manufacturer of the Salk polio vaccine had failed to properly inactivate the virus, leading to the deaths of 11 children, and 250 cases of paralysis. This led to a temporary drop in vaccine confidence, and the adoption of Sabin's less dangerous oral vaccine across the USSR and other non-US countries. Despite opposition from the March of Dimes, Sabin's vaccine replaced Salk's vaccine in the 60s.