It wouldn't. If anything, it usually does the opposite. Killing the president just makes him a martyr for whatever causes he might've had - usually his party gets way more done without him.

[It all seems obvious enough to the Balladeer. Even with people who might've had a point somewhere, like Leon "Eat the Rich" Czolgosz, it was just...violence for violence's sake, at the end of the day. Didn't change anything except to make the world a bit worse.]

Heck, Garfield's vice-president hated him, but after he died, the guy turned around and pushed through all of his civil reforms.