I would think the FIRST state to try to do so would face overwhelming opposition as the fedgov would very accurately see this as the start of a domino effect. Their response would be limited by a great many factors though: what troops would be used, would said troops be willing to fight in what would be a civil war, and can they even afford it anymore considering how thin the armed forces are stretched as it is?

If it is a well-armed and geographically large state like Texas, the fedgov would likely ultimately fail (especially if other individual states...or groups of states take this as a green light and create a civil war on multiple fronts). If it were a state like Vermont (and they stood alone) the fedgov would likely prevail and thus squash attempts by other states by force of example.