More can always be said, but you may be interested in this previous answer of mine to a similar question.

The shorter version is that there was a lot of confusion over the extent of FDR's health issues, because the Democrats were afraid the Republicans would use it as a political attack, so they tried to keep it out of the public eye. The Democrats had legitimate reason for concern, because the Republicans did try to use FDR's condition against him on occasion. It was mentioned in the press infrequently, and photographs of him in a wheelchair were published a couple times during his presidency, including one in Life magazine on August 16, 1937. FDR and the White House didn't necessarily deny that he had paralytic health problems, but they did their best to avoid discussing them.

The full extent of FDR's health issues wasn't fully communicated to the public until after his death, when detailed in an authorized biography, and mentioned in Eleanor Roosevelt's autobiography. During his lifetime, people knew he'd had some kind of polio-related issue, but largely, the public perception was that he had overcome whatever issues he'd had. This led to some incongruous depictions of FDR during his presidency, such as in the cartoon "Confidence" from 1933 starring Oswald the Lucky Rabbit.