No serious arguments against the illegality and reasons Lincoln started his illegal war yet, so we can review the diaries of the Constitutional Convention and get a sense of whether or not the 'Founders' claimed secession was illegal. Such proposals were made, but rejected. See pages 44 to 47 of Max Farrand's compilation of the proceedings and Madison's rejection of a proposal that the federal government be empowered to use military force to suppress a state's secession:
"A Union of the States containing such an ingredient seemed to provide for its own destruction. The use of force against a state, would look more like a declaration of war than an infliction of punishment, and would probably be considered by the party attacked as a dissolution of all previous compacts by which it might be bound."
The Records of the Federal Convention, Vol.1 page 47, Yale University Press 1911.
"A Union of the States containing such an ingredient seemed to provide for its own destruction. The use of force against a state, would look more like a declaration of war than an infliction of punishment, and would probably be considered by the party attacked as a dissolution of all previous compacts by which it might be bound."
The Records of the Federal Convention, Vol.1 page 47, Yale University Press 1911.