THE COOK COUNTY Organization. The very words brought both envy and reverence to a generation of Democratic country chairmen, and a lot of Republicans as well. Under the leadership of six-term Chicago Major Richard J. Daley, the Cook County Organization was respected for its discipline and its delivery of Democratic majorities on Election Day.

Last Tuesday, the Cook County organization suffered several serious body blows. In the presidential primary, Sen. Edward Kennedy, its endorsed candidate, lost the county by 408,000 votes to Rpesident Carter (who was lucky enough to lose the organization's endorsement). If, as the old line goes, all business is local, then the state's attorney contest in the same Democratic primary was an even more grevious setback. In that race, the endorsed candidate was crushed by the anti-organization candidate, who now not only is a favorite for election to that sensitive office in November, but must also be considered a serious 1983 challenger to the organization's de facto head, Mayor Jane Byrne. The name of this young maverick who humiliated the Cook County organization: Richard M. Daley, the son of the late mayor.

The mayor himself, a man with a very sensitive feel for such things, knew in 1976 that the day of the organization had already passed; he endorsed Jimmy Carter on the last day of the primary season, after Mr. Carter had carried Ohio. The major was a gifted political reader. If several million other people equated this talent with being powerful political leader, then far be it from him to correct them.

When the results from this year's Illinois primary proved is that American voters are increasingly independent people. They make up their own minds on the candidates and are not generally deliverable, even by the legendary Cook County organization. This news will come as a real blow, we know, to legions of people who were already planning their campaigns agsinst "the clubhouse crowd" and/or the "political bosses." Just add this one to the growing list of shortages we face: political machines.