Here's a headline from the Los Angeles Times of July 5, 1960--just before the Democratic convention convened in our fair city: KENNEDY REJECTS ALL SUGGESTIONS HE QUIT Senator Also Denies Convention Is Slanted to Nominate Him.
Now that's funny, because he'd won ten of the 15 primaries that year (Hubert Humphrey won two but had already withdrawn from the race, and the other three primaries went to "favorite son" candidates). Why would he deny that the convention was slanted in his direction?
As for the suggestion he step aside, JFK was responding to President Truman's "suggestion of whether Kennedy had the experience and maturity for the nation's highest office, [by] asserting that people were looking for 'a new generation of leadership.'"
Nothing ever changes, huh?