Lyndon Johnson rose to power after that fateful day in Dallas. He was elected on his own right in 1964 and saw the high water mark of his administration shortly thereafter as his beloved Great Society was shouldered aside by concerns about the Vietnam War.
Johnson was a master negotiator, having worked his way up from the back row to the heads of every organization he'd be affiliated with from his college student government, the state of Texas and finally the U.S. House and Senate leadership.
When he ran for office in 1964 Hubert H. Humphrey, the senator from Minnesota was also on the ticket. Humphrey was in the party leadership before serving as the vice president, he ran (and failed to reach) the Democratic nomination for president in 1952 and 1960, which is why you see his button here.
Humphrey is another one of those men who's tone is still felt in modern politics all these years later. It was the Minnesotan who issued a call for civil rights and liberties as a party platform in 1948. Southern Democrats left the party, miscalculated and found themselves diminished as the nation elected Harry Truman to office.
Johnson felt shut out when he was John Kennedy's vice president, and made sure to include Humphrey by threatening his own ambitions for the Oval Office if he didn't support Johnson on Vietnam.
Johnson retired from public office during his 1968 run, amid concerns within the party, infighting and the ever-present Robert F. Kennedy. Their antagonistic relationship makes their jugate button unusual to say the least. Johnson died in 1973. Humphrey became a professor and returned to the Senate. He'd run for the White House again in 1972 and 1976 before dying in 1978.
Personally, I find the Johnson designs are some of the finest cellophane from the mid-20th Century. Not the disembodied head one though; those are just creepy.
Everything I know about LBJ is from Doris Kearns Goodwin.