I think that Obama should tell the individual states that if any state holds an election on the matter for its general public and more than 2/3 of the voters in that state wish to leave the US, that he will honor the decision and let them depart. A transition would be required to remove any military equipment and the like. But we do not want to hold states that are so convinced that we work against their interests.
Now, I would require a supermajority because I wan t the state to be in solid agreement that this is the right course of action. When the colonies separated from England, they did not do so lightly. I suspect some of the states are simply unhappy that their preferred candidate lost the election. That is a very shallow reason. It is also a reason that will likely to result in internal strife within the state after separation. People don’t agree on everything.