Like some of the others who have posted, I was also a Navy Nuke. As has been stated, this is the hardest school set in the Navy. I was also a submariner. I also have a friend who is in Nuclear Field EM "A" School right now. To answer a question asked earlier, if the NAVY fails to get you into the schools you have signed a contract for, you can get out of the Navy. This is actually likely to happen to my friend. He is a little older than most going into the military, and has managed to completely ruin his credit rating (and when I say ruin, I really mean RUIN, I think it's barely above 100). Because of this, he will not likely be able to get his security clearance. Without a security clearance, he will not be able to go to Power School, and that will mean that the Navy will be in breach of contract, and he will be given the option of changing rates (hard to find a decent one without a security clearance) or getting out of the Navy.
That being said, if the person going through the school doesn't make it (and academics are only one of a myriad of ways that this can happen), that person is still obligated to the remainder of his/her contract (and yes, women CAN be in the nuke program now, though this didn't used to be the case).
The nuclear pipeline is the toughest in the Navy, and there are many ways to wash out. Get caught drinking underage and you're out. Go nuts (and this isn't uncommon, Nuke school is the most stressful school I have ever been in) and you're out. There are many other ways. A couple of stories from when I was in Nuke school: One friend of mine got walking pneumonia, still had to do PT, and because of sheer exhaustion was not able to keep up. Technically, he failed out, but he could have been put back a class or two because he HAD been very sick and could prove it. They just wouldn't do it. Another guy was going through the checkout at the Exchange and the checkout girl missed something he was buying, as did he, but the chief (might have been a senior chief) behind him didn't. The chief also didn't say anything til this guy was out the door, making it theft. This guy was booted from the program (he was in my class, and we were about to graduate from A school). Another guy, who was the top guy in my A school class at the time, just flipped out. He asked my roommate if he could borrow his car to go to the airport so he could change his ticket home(we had just been informed of a change in our holiday schedule, so this made sense). Guy wasn't seen for nearly six months. They found him in NY, I think. Only reason they found him is cause he stole plates from a car in NJ, and those were on the car.
This isn't to run down the Nuke program, just saying that they have strict standards, it's a stressful environment, and they are (rightfully, in my mind) very anal about the rules.
About the work that you would do once in the fleet. I only know it from the submarine side, but that is very different from the surface side from everything I have heard. I was in a fast attack sub, which is also a lot different than a missile sub. On a fast attack, you are in and out of port. It is unusual to be out of port for more than a month. The exception to this is deployment. Deployment could be a Med cruise, or a Westpac. I was stationed on the west coast, so we did a Westpac. Basically, we were away from our home port for 6 months, doing a number of different things. I can say where we went, mostly, but not what we did, as I think that stuff is still all classified. We went to Japan, then to Guam, then we went on our spec-op (special operation, when we were out to sea for 67 days), then back to Guam (this was supposed to be the Philipines(sp?), but Mount Pinatubo(sp?) blew its top right as we were coming off spec-op and it was unsafe to go there), then to Australia, back to Guam, and finally back to our home port (which was Hawaii). For a good bit of this, I stood port and starboard watches (6 on, 6 off). On top of that, I had other duties, so I was lucky to get 6 hours of sleep a day.
Hmm, it's lunch time, think that's all for now.