Warnberg,
As long as you don't call it quits they will work with you until you develop the skills and they feel you can accomplish it.
If you enter the pool with a "what if" doubt in you mind you will psychologically place yourself at a disadvantage.
Just enter the water calmly and have a positive attitude and you'll do fine. I completed my pool dives and took my written exam just this past weekend and I do my ocean dives this Sat and Sun.
So just like you I am asking myself the same questions but keeping my mind clear that I will go in with a positive attitude and remain calm at all times.
While doing one of my excersizes in the pool I almost panicked but I kept calmed and allowed my instructor to aid me, as I remained calm everything worked out just fine and I was able to rebound and complete the task.
It's about trusting your instructor and that is why they say you can ask all sorts of questions about what certification is the best, PADI, SSI, SDI to name a few and they will always say; it's all about the instructor and how comfortable you feel with him or her.
I think you will do fine since you said you have snorkeled, that's one of the requirements under SSI that I had to perform in the pool last Sunday.
By the way, I asked you earlier what part of Tampa you are training? The reason I ask is that I have family, my mom and younger brother live in Apollo beach and my bro always talks about how nice the areas are regarding scuba diving.
MG