George Washington was elected first President, as all had anticipated, under the new Constitution.  John Adams was the Vice President, Thomas Jefferson the Secretary of State, and Alexander Hamilton the Secretary of the Treasury.  Madison was in the House of Representatives serving as Washington's floor leader and right hand man.

Hamilton, however, developed economic proposals that Madison thought went beyond the enumerated powers of the Federal government. Madison argued that the doctrines advanced by Alexander Hamilton in his Report on Manufactures subverted "the fundamental and characteristic principle" of the federal government:

"If Congress can do whatever in their discretion can be done by money, and will promote the General Welfare, the Government is no longer a limited one, possessing enumerated powers, but an indefinite one, subject to particular exceptions." Madison, Letter to Edmund Pendleton, January 21, 1792 (Madison 1865, I, page 546)

Washington listened to both sides, but eventually backed Hamilton.  Hamilton became the dominant force in the cabinet and was regarded by some as Washington's Prime Minister.

Madison had worked with Hamilton in the Congress under the Confederation, at the Annapolis Convention, and for the ratification of the Constitution in New York State.  Nonetheless, Madison broke with Hamilton over the economic policies and went into opposition to the Federalists.  He was joined by Jefferson, and they sought to form a new party with the philosophy of a narrow interpretation of the powers of the federal government. 

The logic of the Electoral College dictated that Jefferson and Madison look for allies in large, northern states, and they found them in New York.  "Politics makes strange bedfellows" and Madison, now arguing for a less active federal government, found himself allied with some who had opposed the new Constitution.  Nonetheless, Jefferson and Madison created a new party, the Democratic-Republican party, in opposition to the Federalists.  Madison thus played a key role in the creation of the first two party system.