The Army, Air Force, Navy, Marines, and Space Force are all covered by the dictates of the restrictions of posse comitatus law. The Coast Guard is not… early on I believe it was the United States Revenue Cutter Service under the Department of the Treasury, and now is managed by the Department of Homeland Security.
Posse comitatus originally related to counties (see the earlier mention of the counties prior to the American Revolutionary War).
In case of a serious secession movement in NH (or anywhere else), the National Guard is the ones to watch.
So long as we do not become violent, or use force to keep federal officials from performing their lawful duties, we should be alright… unless treachery, deceit, negative propaganda, etc. are implemented on the part of of the feds.
The president can request state National Guard troops, but the governors are not required to activate them. National Guard troops from one state can be used in an adjacent state without presidential interference if both states agree.
If the president wants to use National Guard troops from one state in another state, federalizing the National Guard, he can simply ask around for a governor who supports him in that endeavor, and those troops can be used to put down an insurrection in the other state. However, federalizing the National Guard would bring them under the restrictions of posse comitatus. This would apply to the situation that would obtain if New Hampshire declares independence, and the feds lie about violent forces within New Hampshire. The president is allowed to put down insurrection, rebellion, etc. in a state wherein state officials are either unable or unwilling to put down the rebellion.
Something like the above occurred during the January 6, 2021 “riots” in D.C. There was a request for National Guard troops from the states, but only nine states sent anyone. There is no requirement that governors must to honor such a request.
My guess is that most states in this situation would not want to risk allowing out-of-state National Guard troops into their own state, and so any attempt to garner the approval of Congress would result in an almost unanimous rejection by them. Any president would likely be impeached over taking the action himself, and likely lose his position.
We are then left with civilian federal law enforcement agencies to counter any bid for independence. This would involve DEA, FBI, CIA, IRS, FDA and other alphabet agencies. They would try to find every infraction under their own regulations, and would probably descend en masse at some point.
We would have to be vigilant, for some years before any actual attempt to secede. Intelligence gathering will be paramount. I’m not worried about the weapons that might be used. I’m more concerned about personal, individual, protection protection.