I disagree. Fear is one of the two major forces at work in a startup (the other is faith).
There are legitimate fears--these are the risks. Fear that you'll run out of money. Fear that you've picked the wrong people to work with. Fear that you'll be beat to market. If you don't have some measure of fear, you're ignoring risks, which makes your failure that much more likely.
You definitely need a constant drive, but I don't think it has to be fear.
The fear you should have is not being able to make rent or buy food. You should fear having to go back to your cubicle job or the lecture hall at school. Know that a startup lifestyle is for you, and fear going back to the life you didn't want. Fear these and that will keep you reaching to succeed.
There are legitimate fears--these are the risks. Fear that you'll run out of money. Fear that you've picked the wrong people to work with. Fear that you'll be beat to market. If you don't have some measure of fear, you're ignoring risks, which makes your failure that much more likely.