Very low barrier. Once every couple of years (For the 20 or so).
The first two days the first time you do it are a not comfortable. But other than that, it's no big deal - around the beginning of the 3rd day, you just lose your appetite and food is not appealing anymore for a while.
It only seems like insurmountable because, if the discomfort you feel for a few hours of unsatisfied appetite continued similarly (linearly, parabolically, exponentially - whichever way it feels to you), then it would actually have been insurmountable. But that's not the case.
It's like cold showers - a guy on this board, joel_runyon, advocates 40 days of only-cold showers[1] as, if I understand it correctly, part-physical-part-psychological therapy. Regardless of any specific merits, the only possible cost is a slight discomfort - yet it seems insurmountable to some people.
[1] http://impossiblehq.com/cold-showers-excuses