LBJ had far greater control over the party than Truman did. He was an extremely skilled political operative, and as a southerner himself was able to reach out to other southerners in a way that a northern liberal could not. He was also someone you had to be leery of crossing. Antagonizing LBJ could hurt your political career in Congress in a way that Truman never could. LBJ also had the advantage that he was able to invoke the name of JFK.
So while it is possible someone might defect from the pary and challenge LBJ (like George Wallace did in 1968), that person might as well be ending his political career.