Hamilton and Jefferson were both appointed to Washington's cabinet. Hamilton was the secretary of the treasury and Jefferson became the secretary of state. Creating a cabinet was only one of several precedents set by Washington in areas where the Constituton was silent or unclear.
Hamilton and Jefferson had very different opinions. This undoubtedly caused them to debate heavily during the times they served this position in the government. However, it also gave Washington a wide range of ideas coming from his closest advisors.
During this confusing time of a new government finally in power, political parties also came about. By the election of John Adams, two factions had arisen with very different political values. The Republicans were led by Thomas Jefferson and James Madison. The Federalists were guided by Alexander Hamilton and counted President John Adams among their members.
Hamilton, as a Federalist, believed primarily in a strong central government run mainly by upper-class citizens and the commerce of the nation. He characterized the general public as "selfish, unreasonable, and violent." He idealized that the federal government should encourage the development of American industries. Hamilton proposed a plan to manage the countries debts and to establish a national banking system. Hamilton also proposed to pay off the foreign debt and to issue new bonds to replace the old bonds. One of the most significant things Hamilton did was propose the idea of a national bank that would be funded by the federal government and private investors, and that would also issue money and handle all government funds. During the XYZ affair, the Federalists preferred to fight the French than to pay or negotiate, as the Republican position confirmed. The Federalists also agreed with and helped pass such laws as the Naturalization Act, the Alien Act, and the Sedition