It's called JFK: The Lost Inaugural Gala. The special is footage of the pre-inaugural entertainment for John Kennedy in January, 1961. The description says that the performers include (are you ready?) Frank Sinatra, Ella Fitzgerald, Nat King Cole, Ethel Merman, Gene Kelly, Jimmy Durante and Metropolitan Opera star Helen Traubel (who later in her career starred in Rodgers and Hammerstein's musical Pipe Dream.)
Yowza. Quite the historical document.