The rise of political parties in the 1790's was largely the result of the formation of groups with opposing views about the structure of government. The first two groups were the Federalists, who supported a loose interpretation of the Constitution and a strong central government, and the Republicans, who supported the opposite. These two groups became the first "political parties."
Even before the ratification of the Constitution in 1788, there were debates and arguments about the way in which the Constitution should be interpreted and used. The two groups with differing opinions went on to become the first political parties once the Constitution was finally ratified.
The "official" birth of political parties is due to a feud between Thomas Jefferson and Alexander Hamilton in 1792, according to Dr. Barrow's Online Classroom at Pope John Paul II High School. Hamilton constructed proposals to fund the federal and state debts, to establish a national bank, and to provide government assistance to manufacturing. These proposals were met with opposition. James Madison saw Hamilton's plan as a threat to his ideal vision of America, so he and Thomas Jefferson founded a newspaper to criticize it. In response, Hamilton created his own newspaper, the Gazette of the United States.
Political parties rose out of those who supported each plan. Hamilton's supporters formed the Federalist Party, and his opponents formed the Republican Party, also known as the Democratic Republican Party or Jeffersonian Party.