In 1833, Judge Abel P. Upshur wrote a series of six pamphlets titled "An Exposition of the Virginia Resolutions of 1798", and in them he makes it very clear the importance of keeping the Union together. You can read five of these pamphlets here(1, 3-6) and the second pamphlet is here on page 70. Here's some of what he says:
In the first place, a State which withdraws from the Union breaks the Union. This is true, ex vi termini, and therefore, need not be proved. But I have already shown the Resolutions of 1798, proceed upon the idea, that the Union is to be preserved; and indeed, that is the main object of resistance, as therein contemplated. In this respect, therefore, secession is not a means of resistance within those resolutions.
In the second place, the resistance therein contemplated, must be such as will "arrest the progress of evil." Will you be so obliging to tell me, sir, how a usurped power can be resisted, by giving way to it? In one way, indeed, the evil may be arrested by secession; the usurped power may be rendered nugatory, by withdrawing from its reach, all the subjects upon which it can exercise itself. I can scarcely imagine, however, that this tame and submissive idea, was entertained by the statesmen of 1798. It appears to my humble understanding, that secession, so far from being a form of resistance to usurped power, is the precise reverse; it is neither more nor less than a running away from the oppressor. And so far from "arresting the progress of evil," it encourages and invites the evil, by removing all restraint from the wrong-doer. In this view, therefore, it is not within the resolutions of 1798.