Andrew Johnson was a border state Democrat who was put on the ticket with Lincoln for political reasons. John Tyler had nothing in common with the policies of the Harrison administration, which only lasted for a month.
Q: Yet all of these men landed in the White House after presidents died. When did the political system start taking the vice presidency seriously?
A: The system changed around 1940 when the president became more powerful, the national government looked to do more, and the presidential candidates began to take a role in selecting their running mates. From 1976 on, it became increasingly clear that it was good politics to chose someone who was a plausible successor.
Q: Who are some of your favorite obscure vice presidents?
A: Garret Hobart, an unlikely guy who was McKinley's first vice president, had been a New Jersey state legislator. At that time, vice presidents were very peripheral to the business of government, but Hobart became very friendly with McKinley, and he played something of a role. He was an aberration. There's also Thomas Marshall, Woodrow Wilson's vice president, who compared being vice president to a catatonic state: "He cannot speak; he cannot move; he suffers no pain; and yet he is perfectly conscious of everything that is going on about him."