It should be recognized, that there is a difference between "insurrection" or "rebellion" and the formal withdrawal of a State from the union. A valuable perspective on that distinction was offered by William Rawle, in his 1825 A View of the Constitution of the United States of America (there's a link on my FR home page - see Chapter XXXII, etc). Mr. Rawle was a friend of Washington and Franklin, and was the US Attorney who actually prosecuted some of the insurrectionists responsible for the Whiskey Rebellion. He was also an abolitionist - and an advocate of the right of State secession.
[Jackson quote] An attempt by force of arms to destroy a government is an offense, by whatever means the constitutional compact may have been formed; and such government has the right, by the law of self-defense, to pass acts for punishing the offender, unless that right is modified, restrained, or resumed by the constitutional act.
I always found Mr. Jackson's appeal to a governmental "law of self-defense" to be a clear indication that the federal government was already accumulating undelegated powers and pretensions of sovereignty, even in the early years of the republic. The federal government is a creature of the States and their people; it is "hired help", not the property owner. The federal government possesses only those powers delegated to it by the sovereign people of the States, and can claim no sovereignty of its own. Indeed, the States can extinguish the federal government entirely, in complete compliance with the terms of the existing Constitution, should three-fourths of the States ever decide to do so...
The states did not form the federal government, the people did. That’s why it states “we the people ...”. Remember the whole reason that the articles of confederation were scrapped is because the federal government was too weak under them. States could, and did, ignore laws from congress. This is also why the constitution explicitly states that it is the supreme law of the land and so are any laws or treaties based on it.
If the Constitution is the supreme law of the land, and was formed by all the people of this land, no subset of those people can nullify it’s laws, or nullify the results of an election by simply declaring themselves to be an independent nation. I will once again defer to the wisdom of President Andrew Jackson because I believe he states it both simply and eloquently.
“This right to secede is deduced from the nature of the Constitution, which they say is a compact between sovereign States who have preserved their whole sovereignty, and therefore are subject to no superior; that because they made the compact, they can break it when in their opinion it has been departed from by the other States. Fallacious as this course of reasoning is, it enlists State pride, and finds advocates in the honest prejudices of those who have not studied the nature of our government sufficiently to see the radical error on which it rests.
The people of the United States formed the Constitution, acting through the State legislatures, in making the compact, to meet and discuss its provisions, and acting in separate conventions when they ratified those provisions; but the terms used in its construction show it to be a government in which the people of all the States collectively are represented. We are ONE PEOPLE in the choice of the President and Vice President. Here the States have no other agency than to direct the mode in which the vote shall be given. The candidates having the majority of all the votes are chosen. The electors of a majority of States may have given their votes for one candidate, and yet another may be chosen. The people, then, and not the States, are represented in the executive branch.
The Constitution of the United States, then, forms a government, not a league, and whether it be formed by compact between the States, or in any other manner, its character is the same. It is a government in which ale the people are represented, which operates directly on the people individually, not upon the States; they retained all the power they did not grant. But each State having expressly parted with so many powers as to constitute jointly with the other States a single nation, cannot from that period possess any right to secede, because such secession does not break a league, but destroys the unity of a nation, and any injury to that unity is not only a breach which would result from the contravention of a compact, but it is an offense against the whole Union. To say that any State may at pleasure secede from the Union, is to say that the United States are not a nation.” Andrew Jackson proclamation to the people of South Carolina 1832
Of course this was later upheld by the Supreme Court in the Texas vs White(1869)case. About this it stated,
“The Union of the States never was a purely artificial and arbitrary relation. It began among the Colonies, and grew out of common origin, mutual sympathies, kindred principles, similar interests, and geographical relations. It was confirmed and strengthened by the necessities of war, and received definite form and character and sanction from the Articles of Confederation. By these, the Union was solemnly declared to “be perpetual”. And when these Articles were found to be inadequate to the exigencies of the country, the Constitution was ordained “to form a more perfect Union”. It is difficult to convey the idea of indissoluble unity more clearly than by these words. What can be indissoluble if a perpetual Union, made more perfect, is not?”