I've added a cheap amateur radio HT with FM (but not, unfortunately, AM) broadcast receive capabilities to my laptop bag -- I already had one in each BOB. It's small, got great battery life, it was an easy addition.
I would be surprised if AM stations stayed up very long. FM has way more listeners so way more advertisers and therefore way more $ to be lost if they go down. I would bet they have way more fuel for their backup generators.