OK, but what if the invader's whereabouts and intentions were not known by anyone but the president? Contact with the governor must be made, preferably before the assault, so emergency management can be arranged.
If possible the President would inform the governor of the states involved, and the military commanders would try to coordinate with whatever services they would need, but the military has its own medics, etc., so they wouldn't need much.
The interesting thing here is "...what if the invader's whereabouts and intentions were not known by anyone but the president?"
What kind of invader would only be known to the President? If you are putting aliens or supernatural characters in, then things would not change. If this is your story, then you can have your president do whatever you want him to do. He can bee like W and think that the Constitution is just a piece of paper. The nice thing about writing fiction is that one can have one's character do anything at all.