Clyburn, a veteran of the civil rights fight and longtime participant in state and federal politics, said people forget the difficulties of passing health care.
"The first civil rights bill was very comprehensive," Clyburn said. "In order for the filibuster to be broken we had to drop off the Voting Rights [Act]."
He said there was big disagreement between Congressional leadership and Martin Luther King Jr.
"[President Lyndon] Johnson was very clear, it was not going to get done if they kept voting rights in," he said.
Clyburn did not explicitly draw the link between health care and civil rights, but he's been saying lately he was not confident the public option would survive a final health care bill.
McCaskill (D-MO) also said of health care politics, "Time's on our side," noting her seat isn't up for reelection until 2012.
The call topic itself was fascinating, as Democrats want to take power away from the superdelegates who helped decide the 2008 primary fight between Barack Obama and Hillary Clinton. More on that here.