Announcing a withdrawal from the union, declaring oneself not bound by the law of the land, repudiating debts, seizing and destroying of federal property, forming a rival league, calling for an army, firing on US troops -- these were all serious violations of the Constitution. Not abiding with the Dred Scot decision -- if that's what happened was a lesser matter. Perhaps the government would have been with it's right to impose the decision on the states but it's hardly the same as what happened in 1861.
But seriously, the states were virtually autonomous before the Civil War.
But seriously, they weren't. They didn't have the right to coin money, deliver mail, raise an army, declare war, or make treaties with foreign powers. They'd given up a lot of power and the attributes of sovereignty.
The only federal official the people knew was the postmaster.
The hand of government -- especially the federally government -- was light in early 19th century America, but that doesn't mean that the states were sovereign, or that the federal government didn't have powers of its own under the constitution.
Secession was just the next step and not specifically proscribed by the Constitution.
Look at the supremacy clause of the Constitution -- the Constitution and federal laws take presidence over state laws in the federal sphere. Any change in the status of a state couldn't be achieved by the state alone. A "right to secession" was something read into the Constitution by a loose and sloppy reading of the document.
What settled the matter was military action. The Civil War was a second Revolution, but this time the rebels lost.
The revolutionaries of 1776 could make a far better case than the rebels of 1861. In 1776 the colonists had no voice in Parliament. They believed that they had no other way to influence things but to demonstrate and petition. When that channel was closed by the Crown's military action, they took up arms.
The secessionists of 1861 had been represented in Congress -- even overrepresented. They had plenty of channels to resolve things peacefully. But they rejected such Constitutional channels, and unconstitutionally broke with the rest of the country.