An overworked stork (a clear Jimmy Durante caricature) is getting drunk in the Stork's Club ("I do all the woik...and the fadders get all the credit!"). There is an emergency delivery in which inexperienced animals take the babies to their parents. As a result, babies are being sent to the wrong parents (such as a baby hippopotamus to a Scottish Terrier, a baby alligator to a pig and a baby skunk to a goose. To clear up the confusion, Porky Pig is brought in to manage the factory, with Daffy Duck as his assistant. The babies are seen going through a conveyor belt (to the tune of Raymond Scott's famous "Powerhouse") and sent by various animals, while Daffy mans the phones (making quick references to Bing Crosby (who had four sons), Eddie Cantor (five daughters and no sons) and the Dionne Quintuplets ("Mr. Dionne, puh-leeze!!", is Daffy's shocked reaction).
When a stray egg is found without an address, Porky decides to have Daffy sit on it until it hatches. However, Daffy (nor Porky, for some reason) refuses to sit around on top of an egg. Porky chases Daffy around the factory (complete with an imitation of Porky by Daffy), until they wind up stuck on the conveyor belt. The belt winds up stuffing both of them into one package (with Porky as the legs and Daffy as the top half) and send them off to Africa, where a gorilla is waiting for her arrival. When the gorilla looks at the "baby," Porky peeks through the diaper, causing the gorilla to cry on the telephone, "Mr. Anthony, I have a problem!!" (a reference to John J. Anthony, who conducted a daily radio advice program at the time, The Goodwill Hour; its stock phrase was, "I have a problem, Mr. Anthony").
On the Turner Entertainment "dubbed" version (except for Cartoon Network's The Bob Clampett Show where cartoons aired uncut), partially removed was the baby alligator delivered to the mother pig, so that the cut did not seem as abrupt as it is when the cartoon is unedited here. Also removed was the scene near the beginning of the cartoon, with the drunken stork at the Stork Club (though that was only removed on Cartoon Network versions of the short that aired outside of The Bob Clampett Show).
The original version of the pig and alligator scene had a close up shot of the mother pig telling the baby alligator "Don't touch that dial!" This was removed before its theatrical release for being too suggestive. The shot is now considered lost as the release on the Golden Collection never restored it.