I don't know what to make of this article. It's pretty vague. I'd like to hear from someone from the state to see what's actually happening.
Just my .02 but the Article quoted by FarmerRick states "the mayor is hereby authorized to take one or more of the following specified measures throughout the city or any part thereof"
Reading this, if this is the statute being used, seems to mean that under a Governor declared emergency, Mayors are given certain powers, one which MAY be exercised; Item (e) is carrying a firearm basically in a public area. If you believe that ALL of these things will happen, well, do you think they're going to stop selling gasoline (Item d), or close bars(Item c)? I doubt it.
Nebraska's Emergency Management Act gives the governor powers to suspend applicable state statutes and regulations developed by state agencies. In a "Proclamation" as it's known in NE, the governor tends to be rather vague to allow agency heads to determine what statutes, rules, or regulations would need to be waived. Seems odd, but it works.