A week before the Nov. 2 elections for Congress and statewide offices in Illinois, this politically active city is looking ahead four months to the only election that really matters here: the February Democratic primary for mayor.

A recent front-page Chicago Sun-Times opinion poll showed embattled Mayor Jane Byrne trailing likely challenger Richard M. Daley, son of the late six-term mayor and machine boss, with Rep. Harold Washington (D-Ill.) receiving significant support.

Daley and Washington are waiting only until after the votes are counted next week to decide and announce whether they will oppose Byrne in the Feb. 22 Democratic primary, whose winner is virtually assured election as mayor on April 12.

Not since the 1932 election of Mayor Anton Cermak, who was assassinated a year later by an anarchist aiming at the president-elect, Franklin D. Roosevelt, has there been such a wide-open contest.

It likely will test the stength of what remains of the Daley machine, the extent of defections from Byrne of disillusioned anti-machine Democratic voters who helped put her in office, and the ability of Washington to turn Chicago's large block of black voters into a powerful independent political force.

"I'm the most-polled mayor in America," said Byrne when asked about the new Sun-Times survey and previous polls that have shown her popularity fluctuating almost from the time of her election four years ago.

While her opponents said she has been trying to project a more congenial image of cool, caring competence, Byrne insisted voters would reward her for steering Chicago's government and economy through the national recession.

Byrne said the city's finances had been "completely turned around since the the crisis of '79," when she inherited a hidden avalanche of debt.

She took credit for $850 million in public works projects, including a nearly completed extension of the city's rail transit system to O'Hare International Airport, and for $950 million in private construction, including several new apartment towers rising downtown, on the shore of Lake Michigan.

Minimizing the political impact of the city's unemployment rate, which she estimated at just over 10 percent, Byrne said she was proud of several national awards Chicago has recently won for its "liveability," which she said she believed would attract new industry.

Byrne appeared comfortable in her City Hall office, where she vowed she would be still be found after next year's election.

She is surrounded by the kind of large retinue of hangers-on and security men that had helped make Mayor Richard J. Daley a symbol of the vanishing machine politician, and has used the extensive patronage of her office to help amass millions in campaign contributions.

A few blocks away, in the makeshift offices of Richard M. Daley's campaign for state's attorney in the Nov. 2 election, his older brother and campaign manager, William Daley, expressed just as much confidence about the prospect of unseating Byrne. He said the Daley organization's polls showed that she had lost much of her support, particularly among black voters, many of whom he felt could be brought back into the Daley fold.

Painting a far less rosy picture of Chicago's current economic conditions, he said consultants were dubious about its ability to compete with Sun Belt cities in attracting new high technology industries.

Many of the apartment buildings under construction downtown, he argued, were the result of investments made before Byrne became mayor.

In his office on Chicago's south side as the congressman for Illinois' 1st district, Washington was still more pessimistic about conditions in Chicago, particularly among its 40 percent black population.

He has helped lead a voter registration drive this year -- with registration desks in welfare offices, unemployment centers and libraries -- that appears to have added as many as 100,000 new black voters to the rolls in Chicago.

Saying that black neighborhoods are largely ignored by City Hall and that Byrne had made "anti-black" statements, Washington argued that neither Byrne nor Daley could be expected by blacks to do much about their needs.

"They're both interested in the same division of the pie," he said. "She is just more abrasive."