Maybe I'm lucky that in my nuclear power days I never caught a security guy sleeping on the job. The first time I might just make some noise, but I doubt it. For while I don't necessarily think it's a huge security compromise (if someone has made it to your reactor building already this isn't your only security issue), it's definitely something that'll get the plant busted bigtime by any NRC inspector who happens upon it.
Fines are the easy part. Then the usual braying idiots would trot out their usual claptrap, and the clueless buffoons who pass for media would publicize it far beyond its significance. So as a minimum I would have been tempted to make a beeline for his supervisor.
OTOH this security person is probably positioned to make your life miserable too. He and whoever might have been covering for him could say that they'd caught you doing something and guess who's in trouble now?
Security is outsourced at many facilities. If that's true at Turkey Point, there definitely ought to be blisters all up and down their local management's backside. They ought to know how to keep their staff awake - this isn't exactly a new problem with security firms.
But they might have fewer options than you think. One obvious one is security cams at strategic areas. This isn't trivial for a number of regulatory and other reasons that I don't have time to discuss now (some of which involve security...), whether the system is wired or wireless. I'd expect newer plants to have such things in the design, but backfitting them to today's fleet would be awfully expensive.
I haven't set foot inside a nuke plant for over a decade now, so maybe things have changed. But while I was there, NRC inspectors didn't exactly swarmed over the facilities. There was no need to really - day to day operation isn't exciting and shouldn't be. So inspectors would show up in the plant once in a while, but mostly they did paperwork and went to meetings. So if they caught someone sleeping it's pretty sad.
I don't want to hear any excuses for the security guys sleeping. But let's not get too excited about this either.