THEY SAID IT couldn't happen. Even after the old man died Christmas time, 1976, the Chicago Democratic Organization--the only remaining big-city political machine in the nation--pulled itself together under the sure hand and compromising nature of Michael A. Bilandic, a smooth party pro from Daley's own back-of-the-Yards ward. All the nascent fiefdoms popping up across town fell before the power of the new mayor and the still viable party machinery.

Now Bilandic is a loser--a victim of the only force that has ever beaten the Machine in more than 50 years: Mother Nature. It didn't snow inches in Chicago this winter, it snowed feet--seven and a half of them. More than 100 people died of snow-related causes and for six weeks everyone else in Chicago had trouble walking across the street and getting their cars out of their driveways. The incumbent's diminutive challenger, a venomous former consumer sales commissioner by the name of Jane Byrne, branded the Mayor "the Abominable Snowman" for his lackadaisical clean-up efforts and shockingly won an historic victory in Tuesday's voters, raised on an image of "the city and brought thousands more to the polls than expected. The word this week in Chicago is that the weather would not have dared play such games in the old days, the Daley years.

It was to those years that Byrne appealed in her seemingly quixotic campaign run by her husband, a former newspaperman, and a Hyde Park liberal organizer named Don Rose, now considered a traitor by the all-but-dead lakefront independent movement. Byrne was Daley's loyal hand-maiden--willing to sing his praises more loudly and obsequiously than even the most seasoned of ward-heelers. It was she who helped direct the late Mayor's infamous infiltration of dissident groups. When Daley was alive, she was a terror; her acid-tongued remarks stung any who didn't toe the party line. When Daley died, Byrne, who had made few friends in the Machine aside from the boss, lost it all. Bilandic finally fired her as sales commissioner after she made a desperate publicity-grab by accusing him of "greasing the skids" for a taxi fare increase, an as-yet unsubstantiated charge.

The Mayor, meanwhile, seemed fit. He jogged in the second annual Mayor Daley Marathon and his socialite wife lent a much-appreciated cultural air to the city. His fiscal and political leadership proved skillful and he moved to innovate in areas ignored by Daley for years. Polls showed him popular. If not exactly a reform independent, neither was he a hack. Bland was a better word. Chicago politics seemed to be turning into something of a snooze--a change from Daley's iron-fisted but always colorful 20-year reign. Bilandic was considered such a shoo-in that no one but Byrne bothered to challenge him. It was pointless.

THEN CAME THE SNOWS. Bilandic was inexplicably helpless before the elements and voters, raised on an image of "the city that works," grew increasingly irritated. The incumbent tried advertising with a focus on the good times. His T.V. spots featured the sunny lakefront Chicagofest of last summer, when the Mayor was at the peak of his powers. The challenger showed snow-bound commuters and photos of herself with Daley. Laboring under Byrne's verbal barrage and a charge that one of his aides was improperly awarded a no-bid snow-removal contract, Bilandic played the martyr--an ill-advised ploy in a city like Chicago. He compared the attacks against him to the crucifixion of Jesus and the persecution of Jews and blacks.

Even with the snow. Byrne wasn't given much of a chance. She had little money, no precinct organization, no newspaper endorsements. When Chicagoans woke up yesterday to find themselves with a probable new mayor (the April 3 general election is something of a formality), the ironies abounded. Byrne defeated the Daley Machine by cloaking herself in the Daley legacy; she won with the help of black votes when it was Bilandic who had finally addressed the black issues ignored in the Daley years; she will probably become the first big-city woman mayor after a career in which she earned the enmity of women's groups.

The progress of women in politics may well have been set back by her victory. Jane Byrne is mean-spirited, less-than-competent, less-than-intelligent. Her election will mean only the end of the machine's invulnerability, not of its influence in Chicago politics. The city is set up on a weak-mayor, strong-city council system, which with a non-machine mayor suggests a return to the feudal, pre-Daley years when free-wheeling bosses ran wild, getting their hands into more cookie jars than modern-day Chicagoans can imagine even exist. Some of the more wily power-brokers might ally with Byrne and try to co-opt her. In any case, the people of Chicago will face four years of back-stabbing and bickering while this Dragon Lady of the Midwest, her beloved Boss peering down from his City Hall in the sky, grapples gracelessly with the many problems he left her.