The power was put there to suppress rebellion. But a democratic process of secession is not rebellion. Even chief Justice of the Supreme Court Salmon P. Chase said "secession is not rebellion."
States had a right to leave. The Declaration of Independence explicitly says so, and further more, so too does the ratification statements of New York, Virginia and Rhode Island. In addition, during the Hartford Convention of 1814, the states of Connecticut and Massachusetts among others, asserted they had a right to secede, so the understanding of the founding era was that states could become independent if they so choose.
Calling a state referendum on independence "rebellion" is just lying about what is happening.
Secession is not constitutional either; it is not in there. The notion is a rebellion against the Constitution; after all, by joining the Union, a state agreed to be bound by the laws thereby and by declaring to secede, it curses those laws as unjust instead of demanding a proper redress of grievances according to those just laws (when I compare the Confederate constitution to the US Constitution, the problems of the former become very apparent). Citing the Hartford Convention as law is spurious.
BTW, I do not see where Chase saw secession as legal; particularly when it came to Texas, he regarded their joining the Union as “indissoluble”.
I don’t know where you get “state referendum(s) on independence” from; after all, this thread is not about that.