The events of November 1963 and their aftermath are described in Chapter 9 of my undergraduate thesis The Highbrow in American Politics: Arthur M. Schlesinger Jr. and the Role of the Intellectual in Politics.
In brief: Schlesinger, John Kenneth Galbraith, and most of the rest of the White House immediately leaped to the conclusion that “the radical right” was the perpetrator. In the days following the assassination, the Kennedy White House staff split between those who were willing to work for Lyndon Johnson, and those who wanted to find a way to replace him as the the 1964 Democratic nominee with Hubert Humphrey or Robert Kennedy.
Johnson convinced Schlesinger, like almost all of the Kennedy staff, to stay on. But Johnson never gave Schlesinger any assignments, and Schlesinger resigned in early 1964. Schlesinger went to work on a biography of John F. Kennedy (A Thousand Days), and to campaigning on behalf of Robert Kennedy’s successful carpet-bagging run for a New York U.S. Senate seat.
Some observations from half a century later: liberals often had difficulty recognizing their ideological allies. Schlesinger et al. didn’t think Johnson was a liberal, although he turned out to be a much more aggressively liberal President than Kennedy had been. New York liberals, such as Americans for Democratic Action, and Jewish voters, didn’t think Robert Kennedy was a liberal, although as a Senator he (like the Democratic party) became much more liberal than John F. Kennedy had been.
The LBJ-RFK feud had much more to do with personality than with policy. The best study of this is Jeff Shesol’s excellent book Mutual Contempt: Lyndon Johnson, Robert Kennedy, and the Feud that Defined a Decade. Shesol finds plenty of blame on both sides, but ultimately it was RFK who obdurately refused LBJ’s overtures.