In the United States' long history of elections, some elections are seen as pivotal and dramatic (1860, for example), while some are seen as relatively sedate (1996 would be a recent example). The election of 1968, while not being quite as pivotal or dramatic as 1860, is still one of the most dramatic elections in American history, although perhaps "tragedy" would be a better term to use.
Presidential elections in the American system also have two aspects in which they can be dramatic: in terms of the issues and personalities involved, and in terms of the technical working of the election. Not surprisingly, elections with complicated issues and personalities involved are often the ones in which the technical complications of the United States' electoral process are likely to come out, and vice-versa.
The election of 1968 could have become much more complicated than it did. The election of 1968 is somewhat unusual in that the actual election, the day that voting took place and the ballots were counted and the winner announced, was somewhat anti-climactic. The year had already seen the assassination of two of America's most prominent figures, a host of riots, a bloody battle and the decision of a sitting president to not seek another term. But instead of being an anti-climax, the election could have turned into something even more complicated and acrimonious than what had occurred so far.
Richard Nixon finished the election with 301 electoral votes to Hubert Humphrey's 191, and George Wallace's 46. While the electoral margin between Nixon and Humphrey was relatively wide, he won with a plurality, and a margin of .7% . And because there was a third party candidate with some electoral votes, the situation was very close to there being no electoral majority. There were many ways that a shift of a few tens of thousands of votes in certain states could have swung Nixon below the 270 electoral votes needed to win the presidency. There are a number of scenarios in which Wallace or Humphrey or both could have won several states, putting Nixon below the 270 electoral votes.
According to the 12th Amendment of the United States Constitution, if no majority exists in the electoral college, the United States House of Representatives votes amongst the top three recipients of electoral votes. But instead of each representative voting singly, the delegation of each state has one vote, with a majority of states needing to approve of a winner. What this process would have looked like is hard to guess at, other than it would have been messy. At the time of the election, the House had a majority of Democratic representatives, both in total numbers and in states controlled. However, many of those were conservative Democrats from southern states that supported Wallace. Would they have gone with party loyalty and supported Humphrey, or would they have supported Nixon, who was perhaps closer to Wallace's views? How much horse trading and fig leafing could have gone on? What would have been the popular reaction to Humphrey being named President with a minority of the popular and electoral votes? What would have been the effect of Southern Democrats supporting Richard Nixon en masse? If Humphrey's denial of Nixon had come about because he had won Delaware by 500 votes instead of losing it by 7000, what type of recounts and legal challenges would have happened? And, what would this period of indecision and political maneuvering done to a nation that was already badly confused by the events of the past year?
This is simply a series of "What If?" questions, although very plausible ones. They show how an already contentious situation could perhaps have been pushed over into total chaos by seldom used structural features of the American electoral system. Although hopefully we will not be seeing a repeat of 1968 anytime soon, it is not impossible that in the foreseeable future, we will see a contentious election that is "solved" by the provisions of the 12th Amendment.