In presidential elections, how often do members of the same party run in the primaries against the incumbent? The Ken Burns Vietnam documentary has me wondering this since a few politicians tried to go up against LBJ. I was born in 1983 and can't recall if this has happened in my lifetime.
There has being 4 credible primary challenges to incumbent presidents in post-1960 American political history.
1968: Eugene McCarthy against LBJ: LBJ decided to drop out after New Hampshire. Though NH was an LBJ victory, was far closer than he expected (which also caused Robert Kennedy to enter the race a few days later). His general unpopularity, and internal polling showing him very behind in Wisconsin (the next state to hold a primary) caused him to drop out. Though it should be noted that before 1972 the primary system wasn't as meaningful as nowadays and the convention was the place where candidates are chosen. There were rumors that LBJ was planning to capture the nomination at the convention.
1976: Ronald Reagan challenged Gerald Ford: garnering 45.9% of the vote but ultimately losing
1980: Ted Kennedy challenges Jimmy Carter; getting 37.6% of the vote but ultimately losing
1992: Pat Buchanan runs against George H Bush: getting 23% of the vote but ultimately losing
In most electoral cycles there's some sort of challenge to the incumbent, it's just that it's fairly rare that there is a credible challenge.