Article I, Section 8 gives Congress the authority "for calling forth the militia to execute the laws of the union, suppress insurrections and repel invasions".
Succession is not insurrection.
A statewide democratic vote for independence is not a "rebellion" or an "insurrection." Nations have been doing it quite a lot lately, and nobody is accusing England of "rebelling" from the European Union.
The people who called it a "rebellion" and an "insurrection" were simply liars who manipulated people.
Apart from that, the Constitution derives it's just power from the "consent of the governed" as pointed out by the Declaration of Independence.
Once that consent is withdrawn, they have no further authority.