Here is an interesting ABC news report from Sep 2011:

[link to abcnews.go.com]

Jacqueline Kennedy Reveals That JFK Feared an LBJ Presidency

"President John F. Kennedy was so "worried for the country" about the prospect that Vice President Lyndon Johnson might succeed him as president that he'd begun having private conversations about who should become the Democratic Party's standard-bearer in 1968, Jacqueline Kennedy recalled in a series of oral-history interviews recorded in early 1964."

This revelation was apparently from 8 hours of audio tapes recorded by Jackie Kennedy not long after the assassination.
I have heard though that JFK was also considering dropping LBJ in the 1964 run....which would not sit well with that man.