When the word reached the AFL-CIO executive committee meeting here of Rep. Harold Washington's upset victory in the Chicago Democratic mayoral primary, one of the union staff members remarked ruefully, "Well, we were on the wrong side again."

The Chicago Labor Federation gave its official support to Mayor Jane Byrne, but Cook County State's Attorney Richard M. Daley, supposedly her main rival, was able to come up with a good list of independent labor endorsements of his own. Except for a handful of black unionists, Washington was shut out.

This was not the first time that big labor has guessed wrong on a political race. But this gaffe came at a crucial moment, just as the federation's executive committee was reviewing its political operations and its announced plan to make an endorsement in the Democratic presidential race before the end of this year.

It slowed, at least temporarily, the headlong rush of the labor federation to back former vice president Walter F. Mondale.

The immediate beneficiary of the shock wave that went through the meeting was Sen. Alan Cranston of California, who had endorsed the long- shot Washington and was here lobbying the labor officials for support. While glum operatives for Mondale, a Daley backer, sipped their beers, jubilant Cranston aides whipped through the bar, making sure that every unionist was aware of the Chicago upset.

The Mondale people have a plausible argument that he was not so badly hurt even in Chicago by Daley's defeat. Mondale made some points with politicians of all stripes by honoring his commitment to Daley, in return for the support Daley had given the Carter- Mondale side in the 1980 Illinois presidential primary. Washington is critical of Mondale but neutral in the presidential race. The hostile Byrne has been removed from power. And, since Daley retains his present power base as state's attorney, he and his organization can still be of considerable assistance to Mondale when it comes to slating delegates and electing them in next year's Illinois primary.

But the Washington victory underlined the point Cranston had made to the AFL-CIO executive council during his appearance on the day of the Chicago voting. Reminding them that "I've led on key (labor) issues" and consistently backed union-supported legislation, Cranston asked the union presidents to "give me time before you make your decision" on a presidential endorsement. Cranston's plea that the union presidents not count him out of the race just because he trails Mondale badly in current polls was underscored by the news from Chicago. Washington was running in third place in the early polls; he had the smallest treasury and seemingly the weakest organization; but in the end, he won.

Despite this happy coincidence, from Cranston's viewpoint, Mondale emerged from the meeting as the overwhelming favorite for the AFL-CIO endorsement. His support ranges from the most liberal unions to the conservative building trades. His agents here were promoting a bandwagon psychology.

The larger question behind all of this activity is whether the labor endorsement is ultimately going to be a blessing or a burden for the chosen candidate. Douglas Fraser, the head of United Auto Workers, acknowledges that he is "concerned about the endorsement having some negative fallout," particularly if it appears to be the decision of a relative handful of union leaders, without the participation of the members for whom they claim to speak.

Labor is an important Democratic constituency. By some estimates, two of every five Democratic voters in last November's election were members of a union household. Labor's political arm is growing in power and skill. All this makes the endorsement more valuable.

But Washington's upset is a reminder that the voters have a penchant for taking things into their own hands. Byrne had labor's endorsement and the power of city hall; Daley had the backing of both Chicago newspapers; but Washington won.

And in Miami, just down the road from here, on the night after the Chicago primary, former Florida governor Reubin Askew, who has traveled to all 50 states on his seemingly quixotic campaign for the presidential nomination, celebrated his formal entry into the race.

Askew said in an interview that he was not too concerned about the labor endorsement, because "I'm reaching out to people as Americans, not trying for group support that ties your hands."

That kind of message was as unwelcome at Bal Harbour as the news of Harold Washington's victory.