19th Century newspaper baron Horace Greeley is best known for the quote borrowed for the title of this post. As the founder and editor of the New York Tribune (which later merged with the Herald before shutting down in 1966) he was a champion of the Whig, then Republican, antislavery movement. What not as many people remember is that he donated his body to be defeated by Ulysses S. Grant in the 1872 presidential election. Many modern sources list him as a Democrat, but in truth the Democratic Party was so weak during Reconstruction that they endorsed Greeley rather than nominate their own candidate. The general election was therefore a competition between two factions within the GOP, one of which had nominal Democratic support.
That's not the interesting part, though. Greeley is the only major party presidential candidate to drop dead before Electoral votes were cast.
I won't rehash the entire Electoral College system here (here is a primer if you're lost) but its most useful contribution to modern American politics seems to be the introduction of a number of great hypotheticals. With the ages of a number of candidates in this election more than a handful of people have brought up scenarios in which a nominee dies. What happens? It depends a great deal on when they die.
For the sake of argument let's say Clinton and Warren (VP) win the Democratic nomination. Just to facilitate this example. Anything that happens before the Democratic convention would be an easy solution for either party, by the way. Running in the primaries is not strictly necessary to win the nomination if a candidate – Clinton in this example – were to win delegates in the primaries but die before the delegates cast their votes at the convention. Those delegates would become uncommitted, which is the same thing that happens to delegates won in a primary when a candidate drops out. And really, dying before the convention is nothing more than dropping out of the race. Really emphatically.
After the convention but before the election, if either nominee died they would be replaced according to the rules established by the parties. It wouldn't necessarily be the most formal process; in 1972 when Thomas Eagleton was removed from the Democratic ticket, the nominee (George McGovern) was basically told to pick someone else by the Democratic National Committee. There could be a second, smaller convention in which people in leadership positions met to choose someone in the old (pre-1968) convention style. If the VP nominee died, a new person would be chosen. If the presidential nominee died, either the VP nominee could be elevated to the position or a different person could be chosen. It would be kind of a mess.
After the election but before Electoral votes are cast – the Greeley predicament – is a bit more of a problem. Despite the fact that some states have "pledge laws" for Electors that are very likely unenforceable, Electors can vote for whomever they want. In 1872 nobody much cared because Greeley lost the election soundly, but the Electors split between voting for the deceased candidate and voting for an assortment of other politicians. Thanks to the 12th Amendment Electors cast two votes, one for president and one for VP. So, if the Clinton-Warren ticket won and then Clinton died, a plausible solution would be the Electors casting their votes for Warren as president and…it gets interesting. Could they collaborate and choose someone else to serve as VP? If you read Article II of the Constitution there would be nothing to stop them. They could also cast blank ballots for VP and then allow Congress to appoint someone to fill the position, as happened when Gerald Ford was chosen as VP upon the resignation of Spiro Agnew.
The really tricky part is the gap between the casting of Electoral votes and inauguration. It's a period of about 4 weeks, from late December to January 20. Having already received votes from the Electors, neither candidate could be replaced by the Democratic Party at this point. Alternative interpretations of the Constitution would abound, but the clear course of action would be the elevation of the VP-Elect to the position of President-Elect. Technically, I think the process would be the swearing-in of the VP-Elect and then, with the Presidency vacant upon the end of Obama's term, immediately elevated to the presidency. Then Congress would be required to fill the VP spot.
There's a contingency in place for just about any scenario. Nonetheless it should be obvious that losing a candidate at some point during the election – or especially after the election – would be a mess. The territory might not be entirely uncharted but it would be, with respect to Horace G., effectively unprecedented.