The Federalist and Democratic-Republican Parties emerged out of the Washington Administration, from the opposing visions that Thomas Jefferson as Secretary of State and Alexander Hamilton as Secretary of the Treasury each had for the country. Hamilton favored a stronger central government, which would be able to support financial growth. Jefferson, a supporter of States' Rights, was leery of a centralized Federal Government and distrusted the financial elites that tended to align with Hamilton. As the French Revolution unfolded, Hamilton wanted to support the British while Jefferson favored the French. In a sense, these were two mutually incompatible visions of government, and the conflict over these questions got very heated.
The second President, John Adams, was a Federalist. Facing a very divisive political situation (especially with the French Revolution, the war between France and Spain, and the United States' own uneasy position between those two nations), the Federalists passed the Alien and Sedition Acts, which was used as a tool to prosecute their Republican critics. Understandably, this became the source of much controversy.
As has already been said, the election of 1800 utilized a lot of very personal attacks. However, this ran both sides. Just as Jefferson was painted as an Atheist and a pro-Revolutionary radical, so too did the Republicans depict Adams as a kind of monarch in the making (as opposed to the freedom loving Jefferson). Each side tried to paint the other in the worst possible light.