I thank Stephen Pastis who produces the “Pearls Before Swine” cartoons for this expression, although the cartoon in which this expression was featured wasn’t one of his better creations. The expression is used to describe a person in a weak position who can’t prove their argument for lack of a witness or any solid evidence. The Phrase Finder writes “…it’s just a folksy way of describing something that has no support. The metaphor probably refers to furniture…” Stools with four, three, or even just one leg have functionality, “…but a stool without a single leg to stand on was incapable of supporting you!”