In the United States, a state is a constituent political entity that shares its sovereignty with the U.S. federal government. There were 13 states at the time of the American founding, and there are now 50. The U.S. Constitution states that "New States may be admitted by the Congress into this Union" and it forbids a new state to be created out of the territory of an existing state, or merging multiple states into one, without the consent of both Congress and the state legislatures involved.

James Madison certainly supported a national government with more power, especially in finance, ability to fight state encroachment, and minority protection.  However, he also understood from this passage that too much national power was just as dangerous.  Lance Banning writes, "From first to last, however, Madison assumed that powers would be granted by the people only to perform the common business of the nation, that excessive governmental vigor was as incompatible with revolutionary purposes as any of the state abuses he condemned."
Annotated by bacraig on December 09, 2014
In Article 6 of the Virginia Plan, it stated "that the National Legislature ought to be impowered to enjoy the Legislative Rights vested in Congress by the Confederation & moreover to legislate in all cases to which the separate States are incompetent, or in which the harmony of the United States may be interrupted by the exercise of individual Legislation." 

In response, delegates were questioning the vagueness of incompetence.  Although Edmund Randolph felt that the federal government must be stronger, he also was seeking some balance between state and federal power.  Kevin Gutzman observes, "Randolph's former certainty that the state governments were completely devoid of merit had yielded to a more refined desire to see only certain powers entrusted o the federal government, with the residue of power left to the states."
Annotated by bacraig on November 05, 2014
This was Edmund Randolph's last chance to argue about the need for a second convention.  He would not sign the constitution.In a letter written on October 10, 1787, he argues:

"1. It is said in the resolutions which accompany the constitution, that it is to be submitted to a convention of delegates chosen in each State by the people thereof, for their assent and ratification. The meaning of these terms is allowed universally to be, that the convention must either adopt the constitution in the whole, or reject it in the whole, and is positively forbidden to amend, if therefore, I had signed, I should have felt myself bound to be silent as to amendments, and to endeavor to support the constitution without the correction of a letter. With this consequence before my eyes, and with a determination to attempt an amendment, I was taught by a regard for consistency not to sign.

2. My opinion always was, and still is, that every citizen of America, let the crisis be what it may, ought to have a full opportunity to propose, through his representatives, any amendment which in his apprehension, tends to the public welfare. By signing, I should have contradicted this sentiment.

3. A constitution ought to have the hearts of the people on its side. But if at a future day it should be burdensome after having been adopted in the whole, and they should insinuate that it was in some measure forced upon them, by being confined to the single alternative of taking or rejecting it altogether, under my impressions, and with my opinions, I should not be able to justify myself had I signed.

4. I was always satisfied, as I have now experienced, that this great subject would be placed in new lights and attitudes by the criticism of the world, and that no man can assure himself how a constitution will work for a course of years, until at least he shall have heard the observations of the people at large. I also fear more from inaccuracies in a constitution, than from gross errors in any other composition; because our dearest interests are to be regulated by it; and power, if loosely given, especially where it will be interpreted with great latitude, may bring sorrow in its execution. Had I signed with these ideas, I should have virtually shut my ears against the information which I ardently desired.

5. I was afraid that if the constitution was to be submitted to the people, to be wholly adopted or wholly rejected by them, they would not only reject it, but bid a lasting farewell to the union. This formidable event I wished to avert, by keeping myself free to propose amendments, and thus, if possible, to remove the obstacles to an effectual government. But it will be asked, whether all these arguments, were not . . . well weighed in convention. They were, sir, with great candor. Nay, when I called to mind the respectability of those, with whom I was associated, I almost lost confidence in these principles. On other occasions, I should cheerfully have yielded to a majority; on this the fate of thousands yet unborn, enjoined me not to yield until I was convinced.

Again, may I be asked, why the mode pointed out in the constitution for its amendment, may not be a sufficient security against its imperfections, without now arresting it in its progress? My answers are–1. That it is better to amend, while we have the constitution in our power, while the passions of designing men are not yet enlisted, and while a bare majority of the States may amend than to wait for the uncertain assent of three fourths of the States. 2. That a bad feature in government, becomes more and more fixed every day. 3. That frequent changes of a constitution, even if practicable, ought not to be wished, but avoided as much as possible. And 4. That in the present case, it may be questionable, whether, after the particular advantages of its operation shall be discerned, three fourths of the States can be induced to amend."

Annotated by bacraig on October 30, 2014
One of only 3 clauses of Magna Carta still in law, this clause protects London's ability to do such things as elect its own mayor, as well as appoint other officials. This ability to operate on a local level may be an early inspiration for the sort of federalism outlined in the federal Constitution. While the Constitution presupposes the existence of states as political bodies, and it goes a long way toward defining what the relationship between the state and federal governments will be (it names some areas where the federal government is supreme over the states; it names some areas where the states have limited or no jurisdiction; and it specifies some actions or conditions that are forbidden to them and some that are required of them), the Constitution, for the most part, does not dictate to the states how they must conduct their internal affairs. The sort of sovereignty enjoyed by the states nods to the sovereignty expressed to London to "enjoy all its ancient liberties and free customs."Further, granting these liberties and free customs to "all other cities, boroughs, towns, and ports" may be a precursor to Article IV, Section 1 of the U.S. Constitution, which outlines that "Full faith and credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State..." in addition to Article IV, Section 2's provision that "The citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States."
Annotated by jhowell on October 23, 2014