Among the party leaders Mr. Clinton alienated over time by his angry tirades was South Carolina's Rep. Jim Clyburn, the third-ranking House leader and a civil-rights-movement veteran.

Before South Carolina's primary, Mr. Clyburn admonished Sen. Clinton for suggesting President Johnson deserved more credit than Martin Luther King Jr. for civil-rights laws. On primary night, Mr. Clinton called Mr. Clyburn and they spoke for 50 minutes. "Let's just say it wasn't pleasant," Mr....