Many cases are media sensationalized, and it is rare for a person to survive 3 or 4 days without food. More often than not people in these situations dying within the first day or two.
Starvation is plagued with many complications that are both difficult to predict and highly variable from case-to-case, so it is impossible to come up with an exact number of days of survival possible. However, one study estimates an average of just 1 – 3 days before severe health complications result in death. In other words, the answer sits somewhere between “less than 1 day” and “about 2”.