An overwhelming exception is an informal fallacy similar to a hasty generalization. It is a generalization that is accurate, but comes with one or more qualifications which eliminate so many cases that what remains is much less impressive than the initial statement might have led one to believe.
Examples:
"All right, but apart from the sanitation, the medicine, education, wine, public order, irrigation, roads, a fresh water system, and public health, what have the Romans ever done for us?" (The attempted implication (fallacious in this case) is that the Romans did nothing for us). This is a quotation from Monty Python's Life of Brian.
"Our foreign policy has always helped other countries, except of course when it is against our National Interest..." (The false implication is that our foreign policy always helps other countries).
"Well, I promise the answer will always be 'yes.' Unless 'no' is required." (from Madagascar: Escape 2 Africa)
