There must be a great range of values depending on the individual's condition and on the circumstances.
20 to 40 days is possible.
According to Scientific American
At the age of 74 and already slight of build, Mahatma Gandhi, the famous nonviolent campaigner for India's independence, survived 21 days of total starvation while only allowing himself sips of water.
In a 1997 article in the British Medical Journal, Michael Peel, senior medical examiner at the Medical Foundation for the Care of Victims of Torture, cites well-documented studies reporting survivals of other hunger strikers for 28, 36, 38 and 40 days.
Whether politicians making unusual claims should be believed perhaps depends on whether they have reliable corroboration from truly independent and impartial observers. Perhaps he sleepwalked to the kitchen fridge? Is alleged willingness and ability to endure starvation in any way correlated to sound judgement to honesty, integrity or to any other desirable trait in politicians?