Exactly, it wasn't until "dying" in the hallway that Neo truly realized the extent of the "there is no spoon" concept. He was confused after the first bullet and didn't know what to think. The second bullet caught him and he tried to fight the reaction to simply die, which you could see on his face. After that, Smith bombarded him with bullets so that the shock of being shot 2398347 times blocked Neo from keeping a calm, solid perception of "this isn't Really happening." He was consumed by his senses, and because of that, died.

This is the same with the other rebels, and why Neo is the One. The body/mind connection is so strong, that even the strongest of the rebels, (morpheus, trinity, etc) aren't able to defy the body/mind seperation of dying inside the matrix. That is why Neo is the "One" he represents the Exception to the rule; the tiny percentage of the masses that can unobstructedly seperate his consciousness from the sensory assualt that the matrix data gives everyone else.

It is just like in lucid dreaming. If I'm dreaming of something very intense, it's rare that I can keep my lucidity through the entire ordeal. If I start to get more concerned with "how do I handle this" or "damn, this is too much!" I start becoming more invovled with the dream scenario, rather than seeing through it for what it is, a construct of my own mind. It's hard to stay calm and focused when you're experiencing something that would be, in waking life, life threatening, which is what Neo experienced when he died in the hallway in the first movie.