I'm a PICU nurse and definitely not one of the outwardly over protective nurses. When I was a student in the PICU, my nurse told me before we went out to see our first patient that if I touched anything or did anything without her saying it was ok first that she was going to call security and have me escorted out. She ended up being a great preceptor, but I thought that was a bad way to make a first impression!
The first thing I ask my students is if they are interested in ICU nursing. If they say no, I pretty much don't let them do anything, because if they aren't interested, they are less likely to be safe in the critical care environment. So, make sure your preceptor knows you're interested in the ICU and that you want to learn as much as possible. Most ICU nurses like to teach, so if you're interested and receptive, they will work harder to teach you things.
Have some specific goals, so they know what to focus on with you. There is so much going on in an ICU, that there is no way to teach a student even half of what the nurse is thinking about. So, I think it is helpful to just focus on a few basic things while you're there. I usually ask my students to set goals for each day, and then I try to help them focus on whatever they want to learn. Things that I think students should know by the end of their ICU rotation (assuming there's time):
1. Blood gas analysis. Every nurse should have this skill down, so practice while you're there.
2. Ventilator modes and what all of the different settings mean.
3. Understanding inotropes, how they work, things to think about when your patient is on them, etc.
4. 5 rights for medication administration, you can't practice this enough.
5. VS normals and changes. Look at your patient's VS every hour and think, "Am I concerned about any of these numbers?"
Students tend to focus on procedures, but that will come so quickly when you're working that they just aren't a big deal. Understanding the critical thinking necessary to monitor and care for these sick patients is the best thing to focus on, imo.
If your nurse trusts you, she will let you do more. Ways to gain her trust: Ask questions if you don't know something. I expect my students to know nothing at all and am pleasantly surprised anytime they can answer one of my questions. Don't worry about sounding stupid, just ask! Any time you're doing something, verbalize out loud to your nurse what you are doing. If you're checking a med, say out loud each thing you're checking. If you're starting an IV, walk though the steps and what you're doing. This way your nurse will feel comfortable that you aren't going to do something really crazy
If you are meant to be an ICU nurse, you will know it when you get there. My first night in the PICU as a student was about as crazy of a night as you can get, and I knew right away that I was meant to be a PICU nurse. Good luck with your rotation!