With the retirement of Washington, the political parties began their dominance. For many years the parties were more important in choosing the president than even the populace. In congress members of each faction met together and would decide who to support for president. The electors who would choose the president were picked by the states using various different methods including by state legislatures, by popular vote, and in some other ways. The "will of the people" was secondary to the "will of those in power". In fact, popular vote totals weren't even officially kept until 1824!
Because the constitution wasn't written with political parties in mind, this election would be the first of two in a row in which an unexpected situation would develop. At the time, after the electors were chosen they would vote for two candidates for president; no mention of vice president was made on the ballot. After all the votes were tallied, the person with the majority of votes was named president and the runner-up was named vice president. The political parties, however, didn't just run candidates for president. They ran teams of candidates with one person running specifically for the runner-up spot of vice president.
The Federalists in congress met together in caucus and agreed to support Washington's vice president John Adams for president and Thomas Pinckney, a diplomat from South Carolina, for vice president. The Democratic-Republican members met and decided to support former Secretary of State Thomas Jefferson for president and Aaron Burr, a senator from New York, for vice president. After eight years of having to keep their opposition to Washington's policies toned down to avoid the appearance of offending the popular president, the Democratic-Republicans came out swinging against Adams. Jefferson's camp accused the vice president of wanting to go back to the days of the monarchy. Adams accused Jefferson of preying on the fears of the people for votes.
In the end, it was probably the endorsement of Adams by George Washington that decided this close election. Adams received 71 electoral votes and was named president. However, because not every Adams elector voted for his running mate as well, Thomas Jefferson came in second with 68 electoral votes and was named the vice president. This quirk in the system caused by the unforseen rise of political factions would be fixed with the ratification of the 12th Amendment in 1804.