ORIGINAL: RERomine
The Supreme Court used Article IV of the Constitution when it declared secession illegal.
Article IV is a reach if you're arguing the illegality of secession - secession does not always and inevitably involve armed insurrection.
This is obviously still an emotional issue for some people - else we wouldn't have someone in this thread claiming ultimate knowledge of the Constitution without being able to cite supporting Articles (that's not a direct reference to you, RERomine). But the fact is that it was only settled by the results of armed conflict in the Civil War, which utterly destroyed the last vestiges of State Sovereignty in this nation and lead us to the Federal system we have today - right along with its Beltway politics and feeding-tube Federal aid to states that keeps them sedated like some kind of government version of the Matrix.
Sovereignty
The question whether the individual states, particularly the so-called 'Confederate States' of the American Union remained sovereign became a matter of debate in the USA, especially in its first century of existence:
According to the theory of Thomas Jefferson, James Madison and John C. Calhoun, the states had entered into an agreement from which they might withdraw if other parties broke the terms of agreement, and they remained sovereign. These individuals contributed to the theoretical basis for acts of secession, as occurred just before the American Civil War. However, they propounded this as part of a general theory of "nullification," in which a state had the right to refuse to accept any Federal law that it found to be unconstitutional. These self-same southern states accepted that non-slave states had such nullificatory rights, but protested that the Federal government enforce the Fugitive Slave Act over any state's attempt to nullify it-- but only by sanction, never by military force. However the premises of the Act was explicit in the Constitution under Article IV, Section 2, which required that all prisoners or slaves who escaped into other states, must be returned to their state of origin. Some states argued that, in addition to violating the rights of the alleged slave, because the Constiution provided for no mechanism of enforcement by the federal government, it was reserved to the states,
Likewise, according to the theory put forth by James Madison in the Federalist Papers "each State, in ratifying the Constitution, was to be considered as a sovereign body, independent of all others, and only to be bound by its own voluntary act. In this relation, then, the new Constitution [was to be] a federal, and not a national constitution." In the end, Madison likewise compromised with the Anti-federalists to modify the Constitution to protect state sovereignty: At the 1787 constitutional convention a proposal was made to allow the federal government to suppress a seceding state. James Madison rejected it saying, "A Union of the States containing such an ingredient seemed to provide for its own destruction. The use of force against a State would look more like a declaration of war than an infliction of punishment and would probably be considered by the party attacked as a dissolution of all previous compacts by which it might be bound."
During the first half-century after the Constitution was ratified, the right of secession was asserted on several occasions, and various states considered secession (including, for example, the New England states during the War of 1812; in response, not a single state objected on the grounds that such was unlawful. It was not until later, c. 1830, that Andrew Jackson, Joseph Story, Daniel Webster and others began to publish the theory that secession was illegal, and that the United States was a supremely sovereign nation over the various member-states. These writers inspired Lincoln's later declaration that "no state may lawfully get out of the Union by its own mere motion", based on the premise that "the Union is older than the Constitution."
Modern legal scholars, however concur with Madison's initial claims that the states ratified the Constitution acting in the capacity of sovereign nations.
White v. Texas is more of a case regarding contract law and the power of a governor than it is specifically about the right to secede.
Link:
White vs. Texas (U of Texas - SW Historical Society)
