It was the Confederates who were in violation of the Constitution.
Sorry, them New England liberals had been violating the Constitution for many years..
Looky here, Mr. Federalist - Daniel Webster of Massachusetts
If the South were to violate any part of the Constitution intentionally and systematically, and persist in so doing, year after year, and no remedy could be had, would the North be any longer bound by the rest of it? And if the North were deliberately, habitually, and of fixed purpose to disregard one part of it, would the South be bound any longer to observe its other obligations? I have not hesitated to say, and I repeat, that if the Northern States refuse, willfully and deliberately, to carry into effect that part of the Constitution which respects the restoration of fugitive slaves, and Congress provide no remedy, the South would no longer be bound to observe the compact. A bargain cannot be broken on one side and still bind the other side.
Would you care to quote the article and section that says secession is illegal?