Probably the given orders will tell you about that. I guess it will depend on the reason for declaring martial law. There may be reasons that demand to contain people where they are (e.g. disease control). There may also be a requirement to obtain paperworks for travelling.
Is there a standard procedure for special incidents in the USA? In Germany a standard procedure is to listen to radio broadcasts refering to the incident and inform people who might not have received the message. Radio stations have to broadcast those messages upon request.
You may also have to consider the case of having to transit through a state with martial law between your timeshare and your home.