I think it's healthy to be afraid of new projects. Really. Whenever I get a new assignment, when I just get the first sentences of the project description, and I don't know how I'm going to implement it yet, I get those totally human thoughts burning in me: "How the hell are we supposed to do that??", "Are they nuts?", "They want that to do this???" and so on.
To me these are totally healthy thoughts. There's a phrase - "Fear is the best protection mechanism. It keeps us on our toes". If you're going into a project with a totally peaceful mind and you think you know exactly how its going to end up or what you're going to do - you're preparing yourself for a nasty surprise. There are no guarantees in life. Especially in the software industry. 70-80% of all software projects world wide are either failing miserably at hitting the target end date or being cancelled all together. It is that unpredictable. Mostly because of the way we are used to doing things. Even the best of us.
Agile methodologies try to solve this problem with various countermeasures. They also succeed - to a degree. But no one can ever tell themselves "this is going to be just fine and dandy. I have nothing to worry about". na-ah. Managing project risks is all about doing the worries beforehand and taking care of the "what happens if"s before the happen. That's a healthy worry.
If you're not worried when you start a project - you better start. And you better not stop worrying until you actually finish it , ship it and... wait - now you need to ship version 2.0, don't you? :) let the vicious circle begin.