They would mobilize the military to put down any pro-secession movement. My brain is faltering right now but we actually have a law that covers this.... let me hit the google-nator for a sec.
Ah yes, Ok its
not a law but something that was added to the constitution via the 14th amendment after the Civil War. Basically it defines what constitutes national citizenship.
Why does this matter?
Here is the actual wording of the amendment:
From a constitutional law point, a state seceeding from the Union would abridge the federal rights of its citizens by forming a new state. So technically that would make the entire process of secession illegal. Hence Congress or the President being authorized to send troops to stop such an illegal act.
It's interesting to note that prior to the Civil War there was no definition of what constitutes American citizenship or nationality. It's pretty obvious why they added it, right?
One other thing I noticed while trying to find this information is that there are ALOT of sites on the web about fringe groups in southern states wanting to seceed from the Union. I sort of wish they would actually - all they do is soak up northern states tax dollars and pollute our nation with their 19th century ideas ><