What is this an example of: "I couldn't fail not to disagree with you less"?
Eisenhower used it constantly to fend off reporters. Is there a term to describe this type of phrase?
I think it's a rather extreme case of litotes. From the New Oxford American Dictionary:
ironical understatement in which an affirmative is expressed by the negative of its contrary (e.g., you won't be sorry, meaning you'll be glad).