So is New Hampshire going to set itself up as a separate nation? And have an Army? A navy?
They would be a sovereign independent state, out of the union of the United States of America. ALL states are sovereign states. If the federal government ever went away, the states would still function and exist because they CREATED the federal government and gave the federal government certain powers they had originally. States pre-existed the federal government. On our current course they will outlive it as well.
And they already have a state guard (NH national guard) under the control of the governor. They would also have a militia as defined in their constitution probably defining it as able-bodied men or persons between 18-42 years old.