The United States Constitution guarantees each State a Republican form of government. The President is obligated to use the powers of his office to execute that promise. When Lincoln issued his call for troops after the attack on Fort Sumter he invoked the Militia Act.
"Sec. 2. And be it further enacted, That whenever the laws of the United States shall be opposed or the execution thereof obstructed, in any state, by combinations too powerful to be suppressed by the ordinary course of judicial proceedings, or by the powers vested in the marshals by this act, [words requiring notification by an associate justice or district judge were omitted in 1795 revision. The revision gave the President more authority] the same being notified to the President of the United States, by an associate justice or the district judge, it shall be lawful for the President of the United States to call forth the militia of such state to suppress such combinations, and to cause the laws to be duly executed. And if the militia of a state, where such combinations may happen, shall refuse, or be insufficient to suppress the same, it shall be lawful for the President, if the legislature of the United States be not in session, to call forth and employ such numbers of the militia of any other state or states most convenient thereto, as may be necessary, and the use of militia, so to be called forth, may be continued, if necessary, until the expiration of thirty days after the commencement of the ensuing session."Lincoln thereby declared that combinations to powerful to resist had seized control of the governments in the secessionist States and that the United States Marshals were unable to carry out their duties.
"WAR DEPARTMENT, WASHINGTON, April -, 1861. "SIR,—Under the Act of Congress 'for calling forth the militia to execute the laws of the Union, suppress insurrections; repel invasions,' etc., approved February 28, 1795, I have the honor to request your Excellency to cause to be immediately detached from the militia of your State the quota designated in the table below, to serve as infantry or riflemen for the period of three months, unless sooner discharged.In effect Lincoln declared that the Southern States had succumbed to a putsch that had been effected by an anti-democratic conspiracy. This was a legal fiction because no one had previously claimed that the governments that passed the instruments of secession had been elected contrary to their existing State Constitutions or that those instruments were not Republican in form.
"Your Excellency will please communicate to me the time at or about which your quota will be expected at its rendezvous, as it will be met as soon as practicable by an officer or officers to muster it into the service and pay of the United States. At the same time the oath of fidelity to the United States will be administered to every officer and man.
"The mustering officer will be instructed to receive no man under the rank of commissioned officer who is in years apparently over forty-five or under eighteen, or who is not in physical strength and vigor."
The one case where the case can be strongly made that a state was separated from the Union contrary to it's own governing principles and as a result of a minority conspiracy was North Carolina. They only seceded after the surrounding states had and a Confederate army had occupied them. Citizens of the Tar Heel state will go to great lengths to ensure that they are not confused with their neighbor to the south. Lincoln made a good case for the illegality of secession in his War Message. He was a competent lawyer.
Very few people asserted prior to 1860 that there was no right to secede. Most people argued that it would be unwise and the affection for the Union was wide and deep in all parts of the country, including most of the South. The question of such a dissolution could be effected without prejudice to the rights of other states is a lacuna within the Constitution. There are others. For example the entire concept of Judicial Review arises from a black hole in that it was simply asserted and then left dormant for decades.
The concept of Universal Sovereignty only became established with the adoption of the Reconstruction Amendments, which as has been noted even then did not include women. The doctrine of "one man, one vote", while based on the XIVth Amendment, was not made the law of the land until the 1960s. So under the law as it existed in 1860 it was possible to consider the governments in effect as legitimate.
There is little doubt that the Fugitive Slave Act was becoming unenforceable and that the Southern states were facing a legal and financial catastrophe by 1860. There is little doubt that despite all their arguments about State versus Federal power the governing interests in the South were engaged in a dispute that they could not win with the ordinary majority of free citizens of the North. It was the South that attempted to use the federal government to enforce their local institutions and laws. Failing to do so they then attempted to withdraw and impose a barrier to commerce and transit so as to discourage the erosion of slavery. Their position was not only morally indefensible but economically and physically untenable. They destroyed their own communities and the principles of local government they purported to defend.
My wish is to see some of the gaps in the US Constitution filled to strengthen the institutions that defend liberty and limited government. It is not necessary to revisit the issues on which the Civil War was fought to do so. The XVIIth Amendment that took the election of Senators away from the State legislators, and reduced the States to administrative cogs and agents of the federal bureaucracy, should be repealed. The Electoral College should be made a permanent standing body with the senior representatives of the executive legislature and judiciary for each state members ex officio. The power of judicial review should be transferred to the Electoral College empowered to act a s a court of review. Referral of a law for such review could be made by either the Supreme Court or by petition of a third of the States.