I did some Net research.
In 1968, that year we seem to always look back at as a point where things went wrong, he gave a talk on the Voice of America radio network that beamed out to sixty countries.
"There's no question about it," the attorney general said. "In the next 40 years a Negro can achieve the same position that my brother has." ... Kennedy said that prejudice exists and probably will continue to ... "But we have tried to make progress and we are making progress. We are not going to accept the status quo."
Robert F. Kennedy, Washington Post, May 27, 1968
Of course, when Barack Obama was elected in 2008, 40 years after the comment, it was seen as an incredibly accurate prediction.
According to snopes.com, the Post version "fudges a few details." Specifically, that RFK actually said less specifically "in the next thirty or forty years" and the speech was given in May 1961, not 1968.
Of course, the larger point is that Kennedy and others saw the possibility for positive change during that turbulent decade, and they were correct.