This isn't exactly a political joke, but it does concern a president -

Calvin Coolidge and his wife were touring a model farm. They were being conducted around separately.

When Mrs. Coolidge came to the chicken coop, she noticed that there were 20 hens and only one rooster (cockerel, for our British readers). Thinking this must be some mistake, she asked about this, and was told that one rooster was all that was needed. "Oh, really?" she said, with interest. "And tell me … um … how often does the rooster … um … do his duty?"

"Oh, several times a day," answered the guide.

"Is that right?" said Mrs. Coolidge with amazement, then she thought a minute. "Please," she said, "when Mr. Coolidge comes around, will you be sure he sees this? And will you be sure to tell him the part about the rooster doing his duty several times a day?"

"Certainly," answered the guide.

Mrs. Coolidge and her entourage moved on toward the barn, and a while later, President Coolidge arrived at the chicken coop. "Excuse me, Mr. President," said the guide. "Mrs. Coolidge was here a minute ago, and she asked me especially to point out our rooster. And she especially wanted you to know that the rooster does his duty several times a day."

"Is that a fact?" said the President. "Well, that IS amazing. But tell me, does he do it with the same hen every time?"

"Oh, no," answered the guide. "He does it with a DIFFERENT hen every time."

"Tell THAT to Mrs. Coolidge," said the President.

(I read the above story - I assume it isn't true - in a book called "The Coolidge Effect" by Glenn Wilson, in which the author tries to explain, in biological/evolutionary terms, why males of most species are more promiscuous/polygamous than females.)