I've did three days before, it wasn't a problem. I did it that time for basically the same reason -- to see how long I could go. After the third day I got something to eat because I was literally bored. A week wouldn't be a problem, but I do weigh 235, so I'm not sure how much that affects it. On the third day I just sorta had that empty feeling. Ha ha, I guess it's the truth.
Good luck!
-Lasereth