I think it was a common understanding of the time that if the Declaration of Independence granted states the right to secede from England, then the principles advocated therein also gave them the right to secede from any other political organization.
I recall reading editorials from Northern Newspapers for Southern states to go in peace with their blessings.
I believe that had the Southern States just refrained from provoking the Federals, secession would have been a fait accompli. There was little sentiment in the North to oppose them at the time.
I've seen no writings that indicated that the DOL was anything other than a throwing down of the gauntlet to Great Britain. It had NOTHING to do with secession - it was openly and honestly about outright rebellion.