A massive baby boom is happening in the United States following the end of World War II; a newspaper headline reads "UNPRECEDENTED DEMAND FOR BABIES OVERWORKS STORK!" An overworked stork, who is a caricature of actor Jimmy Durante, is getting drunk in the Stork's Club, saying "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; another headline reads, "NATURALLY SOME SLIGHT MISTAKES HAVE BEEN MADE." A baby hippopotamus has been delivered to a Scottish Terrier, a baby alligator to a pig, a baby skunk to a goose, and so on.
To clear up the confusion, Porky Pig is brought in to manage the factory, with Daffy Duck as his assistant. The babies, including Tweety in a brief cameo, are going along a conveyor belt (to the tune of Raymond Scott's famous "Powerhouse") and sent by various animals via the aid of jet-powered mechanical storks which helps speeds up the baby deliveries, while Daffy mans the phones, making quick references to Bing Crosby, who had four sons, Eddie Cantor, who had five daughters and no sons, and the Dionne Quintuplets. "Mr. Dionne, puh-leeze!!", is Daffy's shocked reaction.
At first, things seem to be going smoothly until a stray egg is found without an address. Porky decides to have Daffy sit on it until it hatches, but Daffy 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 are stuck on the conveyor belt. The belt stuffs both of them into one package, with Porky as the legs and Daffy as the top half, and sends them 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 freak out and to cry on the telephone, "Mr. Anthony, I have a problem!!"
- 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 as of 2001 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.
- The mother gorilla crying out the line "Mr Anthony, I have a problem!" at the ending upon encountering the Daffy/Porky-hybrid "baby" delivered to her is 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"). This Mr. Anthony character was also referenced in "Ain't That Ducky" the previous year.
- When Cartoon Network started airing the 1995 Turner "dubbed version" prints of the pre-1948 Looney Tunes shorts for the first time in 1997, this was the very first cartoon to air as a "dubbed version" on Cartoon Network, replacing the cartoon's a.a.p. print which had aired on the channel (as well as its older sister channels TBS and TNT) in previous years. This cartoon's mid-1990s Turner remaster first debuted on an airing of Cartoon Network's The Bugs and Daffy Show on 11 May 1997.
- A baby bird that resembles Tweety appears on the conveyor belt.