According to Madison, they did.
"It was generally agreed that the objects of the Union could not be secured by any system founded on the principle of a confederation of Sovereign States." -- Madison Explains the Constitution to Jefferson
Their sovereignty was transferred to the people, to be expressed via the popular vote, which elected Congress, and in turn elected the President.
The Constitution was an agreed upon mode of government which gave equal representation to all States in the decision-making process of the central (Federal) government, and laid out a prescribed method of arriving at decisions as a result of the majority will of a Constitutional body, so then, to secede as a result of a disagreement on the decisions arrived at in a Constitutional method by the majority of that Constitutional body, is not to adhere to the State's rights under the Constitution, but a unilateral rejection of the Constitution as a form of government, as well as the Nation it created. A Constitution and government that in the words and minds of they who both wrote it and by signature agreed to have it ordained, were created for the sake of securing "the Blessings of Liberty to ourselves and our Posterity."
A perpetual Union.
Secession was not, IS NOT, a Constitutional right, secession was a unilateral rejection of the Constitution, and the principles their own antecedents died for.
Here is more on Madison just for your info...
Madison fought against the idea of secession in the Nullification crisis and denied Calhoun was correct in his hints that South Carolina could secede from the Union. Madison is often (though not 100% properly) called the "Father of the Constitution" and HE said it was NOT a right. Shouldn't HE know better than either of us if secession was a right?
Here is what he said (And I quote him from my copy of "The Complete Madison" by Saul K. Padover, in which is taken from the Federalist No. LVIII- Fed 22, 1788):
"Lastly, it would facilitate and foster the baneful practice of secessions, a practice which has shown itself even in States where a majority only is required; a practice subversive of all the principles of order and regular government; a practice which leads more directly to public convulsions, and the ruin of popular governments, than any other which has yet been displayed among us."
Further more, in a letter Madison wrote to Nicholas Trist in 1830, Madison said that the Ken. and Vir. resolutions did NOT claim a right of secession but merely meant to deny the constitutionality of the Alien and Sedition Acts. (I got this from my book, "The Last of the Fathers", by Drew McCoy. A great book, but it cost me $60 which was crazy!!)
No Constitution or government was ever created with a clause for its destruction contained within. that means that any consideration that there was an ability to "break the compact legally" is simply NOT one codified into law. Not even the Confederate constitution claimed that secession was a "right" in any way. Even the Confederate Constitution remained mute on the subject.