The debate over what form of government the Constitution established was recorded by multiple delegates in real time. What follows is drawn from those records.
In November and December 1787, James Madison published three essays in The Federalist Papers that defined the terms directly. Federalist No. 10, November 22, 1787, at Yale Avalon:
The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens, and greater sphere of country, over which the latter may be extended.
Madison defined his term directly in the same essay:
A pure democracy, by which I mean a society consisting of a small number of citizens, who assemble and administer the government in person, can admit of no cure for the mischiefs of faction.
Federalist No. 14, November 30, 1787, repeated the distinction:
It is, that in a democracy, the people meet and exercise the government in person; in a republic, they assemble and administer it by their representatives and agents. A democracy, consequently, will be confined to a small spot. A republic may be extended over a large region.
Federalist No. 39, January 16, 1788, defined republic:
We may define a republic to be, or at least may bestow that name on, a government which derives all its powers directly or indirectly from the great body of the people, and is administered by persons holding their offices during pleasure, for a limited period, or during good behaviour.
These published essays were written months after the Convention. The convention floor debates were recorded by Madison himself and by parallel note-takers. Robert Yates of New York kept his own record. Rufus King of Massachusetts kept notes. William Pierce of Georgia kept notes. Their records largely corroborate each other and are each at Yale Avalon.
Madison's convention speech of June 6, 1787, recorded in his own notes:
In a Republican Govt. the Majority if united have always an opportunity. The only remedy is to enlarge the sphere, & thereby divide the community into so great a number of interests & parties, that in the 1st. place a majority will not be likely at the same moment to have a common interest separate from that of the whole.
Madison's convention speech of June 26, 1787, as recorded by Robert Yates:
Mr. Madison was for 7 years — Considers this branch as a check on the democracy.
The Farrand Records, referenced in the Founders Online annotation to the same June 26 debate, quote Madison on the Senate's function:
Landholders ought to have a share in the government, to support these invaluable interests and to balance and check the other. They ought to be so constituted as to protect the minority of the opulent against the majority.
Fifty-five delegates attended the Convention. The debate over how the president should be elected — by direct popular vote, by state legislatures, or by electors — was recorded across multiple sessions. The July 17 debate is at Yale Avalon.
by the people at large... by the freeholders of the Country.
Wilson spoke 168 times at the Convention — second only to Gouverneur Morris. He proposed direct election twice. Both proposals were defeated.
The people are uninformed, and would be misled by a few designing men.
It would be as unnatural to refer the choice of a proper character for chief Magistrate to the people, as it would, to refer a trial of colours to a blind man. The extent of the Country renders it impossible that the people can have the requisite capacity to judge of the respective pretensions of the Candidates.
The people will never be sufficiently informed of characters, and besides will never give a majority of votes to any one man. They will generally vote for some man in their own State, and the largest State will have the best chance for the appointment.
Gentlemen say we need to be rescued from the democracy. But what the means proposed? A democratic assembly is to be checked by a democratic senate, and both these by a democratic chief magistrate. The end will not be answered — the means will not be equal to the object.
Robert Yates recorded Hamilton's speech of June 26, 1787:
Real liberty is neither found in despotism or the extremes of democracy, but in moderate governments. Those who mean to form a solid republican government, ought to proceed to the confines of another government. As long as offices are open to all men, and no constitutional rank is established, it is pure republicanism. But if we incline too much to democracy, we shall soon shoot into a monarchy.
Rufus King's notes from May 31, 1787, document the early position of the Pennsylvania and Virginia delegations on popular election of the legislature:
Mason, Virginia — in favor of popular choice, because the first Branch is to represent the People. We must not go too far. A portion of Democracy should be preserved; our own children in a short time will be among the general mass.
The Constitution uses the word "republican" in its only direct specification of what form of government the states must maintain. Article IV, Section 4, full text at the National Archives:
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
The Constitution Annotated at Congress.gov documents the history of this clause, including the Supreme Court's consistent treatment of Guarantee Clause questions as political rather than judicial — meaning the courts have not defined what "republican form of government" requires in practice.
In 1792, Thomas Jefferson and James Madison organized an opposition party against Hamilton's Federalists. At the time, they and their contemporaries called it "the Republican Party" or "the Republicans." The compound name "Democratic-Republican Party" was applied by historians in the nineteenth and twentieth centuries to distinguish it from the Republican Party founded in 1854. Jefferson and Madison never used that compound name.
On the final day of the Convention, Benjamin Franklin — 81 years old, unable to stand — had James Wilson read a prepared address. The full text is in Madison's notes at Yale Avalon. Three delegates refused to sign the Constitution that day: George Mason and Edmund Randolph of Virginia, and Elbridge Gerry of Massachusetts.
I confess that there are several parts of this constitution which I do not at present approve, but I am not sure I shall never approve them: For having lived long, I have experienced many instances of being obliged by better information, or fuller consideration, to change opinions even on important subjects, which I once thought right, but found to be otherwise.
Thus I consent, Sir, to this Constitution because I expect no better, and because I am not sure that it is not the best. The opinions I have had of its errors, I sacrifice to the public good.
Franklin's address was reprinted in more than forty newspapers before the end of 1787. He did not list his objections to the Constitution at the Convention, and did not state them publicly afterward.
Madison's notes document a separate observation Franklin made as the final signatures were being written:
I have often and often in the course of the Session, and the vicisitudes of my hopes and fears as to its issue, looked at that behind the President without being able to tell whether it was rising or setting: But now at length I have the happiness to know that it is a rising and not a setting Sun.
A separate account of the day is preserved in the journal of James McHenry, a Maryland delegate, now at the Library of Congress Manuscript Division. McHenry recorded an exchange between Franklin and a Philadelphia resident as the delegates departed:
A lady asked Dr. Franklin Well Doctor what have we got a republic or a monarchy — A republic replied the Doctor if you can keep it.