You have to hold the button down for a second or two. You might just have a defective button on your phone.
Correct, hold down the button until you feel the haptic feedback, about 1.5-2 seconds, and the camera app will open. This is to keep you from accidently opening the camera app all the time when you unknowingly hit the button. It is not a defect, but another smart design feature of the Droid.