It is settled legally, that the states do not have the authority to secede, they tried during the Civil War. Many people thought that states could leave the union at that time. However the precedent set by Lincoln's actions are unchallenged now by the legal establishment.

Anyway, the procedure would go like this:

1. State government announces secession.

then

2a. Federal government challenges legality of secession in courts.

3a. Supreme court declares the secession unconstitutional.

Or:

2b. Federal government charges rebels with Treason.

3b. Federal government arrests the secessionists. Using federal troops would likely not be necessary, since national guards are ultimately under the authority of the president, if he calls them up for national service.

Finally, if there was an armed insurrection by natives, they would be put down as domestic terrorists. It would certainly be embarrassing, but not as dangerous as the precedent set by a state leaving the union without a shot fired.

Obviously if the Federal government financially collapses in the next decade, this wouldn't be a problem. But that is very unlikely, since the government has the power to inflate away its debts. With the dollar as global reserve currency, it doesn't really have to worry about an Argentina situation.