That a state cannot secede from the Union?
Maybe Philip can help me out here.
Edit: Before the Civil War
Didn't Vermont try to secede from the union during the early 1800s in opposition to ......I think the war of 1812. There were objections to the secession of Vermont along the lines of "it is unconstitutional". I would look into that further.
I presume you are thinking of the Hartford Convention, but that wasn't really Vermontish in nature. Massachusetts, Connecticut, and Rhode Island had state delegations there, while Vermont and New Hampshire had delegations from some of their counties, but not official state delegations.