You are absolutely correct in saying that people have no constitutional right to revolt. No such concept exists, and it would be preposterous to think of any such right. However, recall that the Constitution is an organic creation of the States acceding to it (ratifying it): The Constitution does not create rights it merely limits the exercise of powers by the general Government, and by the States acceding to its terms. (At least, under its ORIGINAL design, which we are NO LONGER operating under!)
However, recall that the Declaration of Independence states that when " it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation."
In other words, the Declaration of Independence declares that men have the right to dissolve their governments (of which the Constitution is one) and re-establish their political station in a manner which is no longer oppresive.
The only thing absolutely proven by the outcome of the Civil War, is that the Declaration of Independence is absolutely dead to the modern world, and no longer holds any validity, particularly when the Government is entrusted and entitled to vast military powers.
In other words, a Natural Right of Revolution. Note the phrase " Laws of Nature and of Nature's God." The Founding Fathers were under no illusion that they weren't committing treason under British law.
That's the thing about revolutions. You have to win them.