http://www.cdc.gov/vaccines/vpd-vac/polio/dis-faqs.htm
How common was polio in the United States?
Polio was one of the most dreaded childhood diseases of the 20th century in the United States. Periodic epidemics occurred since the late 19th century and they increase in size and frequency in the late 1940s and early 1950s. An average of over 35,000 cases were reported during this time period. With the introduction of Salk inactivated poliovirus vaccine (IPV) in 1955, the number of cases rapidly declined to under 2,500 cases in 1957. By 1965, only 61 cases of paralytic polio were reported.
Is polio still a disease seen in the United States?
The last cases of naturally occurring paralytic polio in the United States were in 1979, when an outbreak occurred among the Amish in several Midwestern states. From 1980 through 1999, there were 162 confirmed cases of paralytic polio cases reported. Of the 162 cases, eight cases were acquired outside the United States and imported. The last imported case caused by wild poliovirus into the United States was reported in 1993. The remaining 154 cases were vaccine-associated paralytic polio (VAPP) caused by live oral poliovirus vaccine (OPV).
So between 1957 and 1965, there were still new cases being reported, although the numbers were much less than in the previous decade.