Frank Pierce, young, drunk, and depressed as shit. His son died a few weeks after winning the election, which colored his Presidency. Speaking of his Presidency, Northerner's hated him for being a weak kneed doughface, Southerner's hated him for not being enough of a doughface, and he was hated by all factions of both parties, so much so he is the only incumbent President to lose renomination. If you have his wife die while in office, he might not be able to take the combined stress of being President and having his beloved wife gone.
Considering his VP died, and he's dead, this would have a profound impact on the next few years, especially considering who the President Pro Tempore is (next in line at the time for the POTUS line of succession).