And if they had attempted to secede the current President at the time would have had constitutional authority to suppress such rebellion and insurrection by armed force if necessary.
Where does the Constitution say that?
As for the constitutional authority to do it- Charles Francis Adams Jr, Union Army veteran and scion of two Massachusetts Presidents, researched and wrote about that after the war in his "The Constitutional Ethics of Secession". He concluded that it wasn't addressed in the Constitution nor the Articles that preceded it and that both the secession and compulsory union sides had valid arguments.