I'll defer to actual paleontologists (or anyone who drops links), but my guess is T-Rex could go a month without food easy. Most modern large reptiles typically go a long time between meals.
Edit: following the intense scholarship in this thread, I have changed my stance. T-Rex probably would not survive a month without food (or water). BUT ALSO, the entity setting the rules and betting 500 mil on it surviving is going to know that. So the Dino's getting fed either way.