I refer you to James Madison's thoughts on the subject:
In forming this compound scheme of Government it was impossible to lose sight of the question, what was to be done in the event of controversies which could not fail to occur, concerning the partition line, between the powers belonging to the Federal and to the State Govts. That some provision ought to be made, was as obvious and as essential, as the task itself was difficult and delicate.That the final decision of such controversies, if left to each of the 13 now 24 members of the Union, must produce a different Constitution & different laws in the States was certain; and that such differences must be destructive of the common Govt. & of the Union itself, was equally certain. The decision of questions between the common agents of the whole & of the parts, could only proceed from the whole, that is from a collective not a separate authority of the parts.
The question then presenting itself could only relate to the least objectionable mode of providing for such occurrences, under the collective authority.
The provision immediately and ordinarily relied on, is manifestly the Supreme Court of the U. S., clothed as it is, with a Jurisdiction "in controversies to which the U. S. shall be a party;" the Court itself being so constituted as to render it independent & impartial in its decisions; [see Federalist, no. 39] whilst other and ulterior resorts would remain in the elective process, in the hands of the people themselves the joint constituents of the parties; and in the provision made by the Constitution for amending itself. All other resorts are extra & ultra constitutional, corresponding to the Ultima Ratio of nations renouncing the ordinary relations of peace.
If the Supreme Court of the U. S. be found or deemed not sufficiently independent and impartial for the trust committed to it, a better Tribunal is a desideratum: But whatever this may be, it must necessarily derive its authority from the whole not from the parts, from the States in some collective not individual capacity. And as some such Tribunal is a vital element, a sine qua non, in an efficient & permanent Govt. the Tribunal existing must be acquiesced in, until a better or more satisfactory one can be substituted.
Letter to Nicholas Trist, 15 Feb. 1830
Of interest here is his reliance on a collective body of the states. I have said before that the slavers would have been on more solid footing had they called for a Constitutional convention. I don't believe their arguments had merit. I believe they were recklessly destroying the Union without cause, but it would have been the republican means of doing things, as opposed to separate conventions.
I need to consider further whether there would be a material difference between a 'constitutional covention' and a convention to debate seccession - assuming each dwelt on the constitutionality of federal action.