Frasier is in the KACL studio, and after taking a call which Roz handles more effectively, grumps about the tedium in his life. Roz gives him two cards to sign, one of which is to go to a fellow employee named Clarence, who's in the hospital for kidney failure. Frasier signs the card, but, thinking it's a birthday card, adds his own personal "wit" to it and hands it back to Roz.
Later, Niles, Frasier, and Martin take a cab to celebrate Martin' birthday, since Frasier's car has broken down. Finding themselves stuck in traffic, Martin strikes up a conversation with their cabbie, who declares that she's pregnant and that her water has just broken. The three men are forced to help her deliver her baby, which arrives moments later in the front seat of the car.
The birthing experience leaves Niles pondering parenthood. In order to help him decide what he wants and whether he's up for the task, Frasier gives him a flour bag to carry around, like high schools sometimes do to simulate a baby. Niles takes his duties very seriously, but Frasier keeps noticing that the bag has patches on it. Niles admits that he accidentally has knocked or kicked the bag about in his carelessness.
Niles arrives at Frasier's with the flour bag burned and tattered, and admits that it caught on fire. As he and Martin and Frasier are discussing parenthood, Eddie gets hold of the flour sack and chews it to pieces on the sofa. Niles mourns it briefly, but admits to Frasier that he realizes now that he doesn't want to be a father quite badly enough.
Meanwhile, Frasier discovers that what he thought was a birthday card was a get-well card for a very sick man, and that he wrote a very inappropriate message about being "nearer to death." Having sneaked into Clarence's hospital room, the stolen card was retrieved, and he and Daphne replicated all the signatures on a duplicate card. Frasier then sneaks back into the hospital room, only to have all the cards hanging over the sick man collapse on him when he tries to hang the card.
Running out of the room, he runs into Clarence, who tells Frasier that he just had his room switched. Frasier attempts to retrieve the card once again, but the groans from the room he's just vacated discourage any further action on his part. Moments later, the cabbie appears with her baby and Niles reflects on fatherhood some more. She lets him hold her baby, and he's enchanted, until he realizes he's hurting the child and that's why it's crying. Frasier agrees that Niles is not ready; however, Niles hangs back a minute to look at the babies in their bassinets.
The final scene is of Daphne cradling a flour sack, Martin making fun of her, and Daphne pelting him with flour.