Is the Windy City's bitter, three-way Democratic primary campaign for mayor dips and curves into its final days, the size and cohesion of Chicago's 650,000-strong black vote are the unknown and possibly decisive factors in Tuesday's election.

Mayor Jane M. Byrne still rates as the front-runner in local polls, but "Calamity Jane's" commanding lead has evaporated despite her ability to spend virtually at will for months from a campaign chest of nearly $10 million--unprecedented for a City Hall primary.

State's Attorney Richard M. Daley, heir to one of the most powerful postwar City Hall machines, continues to make up ground lost last fall when he overconfidently started too late and raised too little money.

He appears to be running second, aided by four debates among the candidates that proved he could speak on his feet. But the margin of difference between Byrne and Daley is too narrow to be significant.

This split has dramatically improved the once long-shot chances of Rep. Harold Washington (D), who is black. If whites who comprise about 60 percent of the city's registered voters are split evenly between Byrne and Daley, Washington might squeak through on a strong black vote. He is saying, "We have it won."

A Gallup poll, conducted for the Chicago Sun-Times and WMAQ-TV and released Friday, puts Washington second to Byrne and gaining ground faster than Daley.

Daley, 40, has scored recently by focusing on Byrne's spending and the role of David Sawyer, the political consultant credited with remaking the mayor's image from that of an erratic and short-tempered person to seasoned chief executive of one of the world's greatest cities.

Last week, Byrne, 48, was hit by allegations that her campaign manager, William Griffin, had a conflict of interest in awarding a lucrative contract for bus service to O'Hare International Airport.

Griffin says it is nonsense. But Daley, despite a reputation for leaving thinking chores to others, recognized an opportunity as quickly as any other local prosecutor seeking higher office and announced an investigation.

The mayor, by nature a scrapper who has picked a fight when she could not find one, seems determined to rest on her laurels and stick to Sawyer's game plan.

"Whether or not this campaign seems like 15 rounds instead of 15 weeks, we're gonna pay no attention!" she told a cheering, standing-room-only crowd of women executives at the Hummingbird Supper Club on the South Side recently. "We've got a good program. We're gonna win!"

She accused the Sun-Times and the Chicago Tribune of "mud-slinging." She is also sore at them on other grounds: both endorsed Daley in editorials denouncing her.

With the stakes and public interest so high, U.S. Attorney Dan K. Webb last week announced formation of an extraordinary task force of FBI and Immigration and Naturalization Service agents, plus U.S. marshals, to patrol polling places and investigate vote fraud complaints Tuesday.

This is not just grandstanding by an ambitious young Republican appointee--"vote early and often" has been an abiding slogan of Chicago elections.

That tradition has been reaffirmed by a massive federal investigation of vote fraud in last November's gubernatorial election.

One of the prize pieces of evidence is a single ballot apparently counted 203 times by enterprising elections officials in a West Side ward who then seem to have thrown out all but one other ballot cast there that day.

Race has always been a factor in the mayoral contest, but, as the importance of the black vote emerged in recent days, Byrne and Daley have said virtually nothing on the subject. Any frontal attack on the 60-year-old Washington might jeopardize whatever strength they have in black wards on the South and West sides. The mayor's organization has predicted that she will receive as much as 30 percent of the black vote. She swamped then-mayor Michael Bilandic in black wards in her upset victory in 1979.

But William Daley, campaign manager for his older brother, dismissed the prediction: "They're nuts, and their campaign is stalled. Things have started to break our way." As for Washington's chances, Daley said, "I don't believe the numbers are there for him to win."

It is a potent line to use on black voters whose candidate received only 11 percent of the vote when he ran for mayor in 1977 and whose campaign has been starved for cash and was short on organization from the beginning.

Byrne and Daley have lined up several endorsements from prominent black ministers preaching realpolitik to their flocks. One night recently, with Daley on hand for a rally at the New Nazareth Baptist Church in southeast Chicago, the Rev. Odell White declared:

"We have to accept reality. We're blocked! We're blocked! Foolish pride is dangerous! Thousands have died to give us the freedom to vote, so don't throw it away. Can't you see why we need Richard Daley on the fifth floor the mayor's office at City Hall ? "

With the message delivered to substantial applause, Daley then concentrated on efforts to combat street crime and teen gang violence.

Washington's rhetoric has shifted recently to concentrate on race.

"It is necessary to bring my community together. We are victims of propaganda, infiltration, lies," he told cheering students in a predominantly black crowd jamming an auditorium at Northeastern Illinois University several days ago.

"We haven't been polarized! There has been bitter suffering, degradation, murder, rape . . . but they haven't destroyed us!," Washington said. "We're courageous, tough, understanding and forgiving . . . . There are 200 or so black mayors in this country, and most are doing extremely well. With 40 percent of the city population, shouldn't we reach out for the Holy Grail? "

The effectiveness of his appeal to blacks to put one of their own in City Hall is crucial, since he does not expect to receive many white votes. "The white vote for me will be 5 to 6 percent," he said. "That's it."

At the same time, since white voters outnumber blacks, 3 to 2, a heavy citywide turnout could overcome any black plurality for him regardless of its size. This puts Washington, who has organized two recent registration drives that added more than 150,000 black voters to city roles, in the somewhat peculiar position of desiring a low turnout.

"We'd be in trouble with a record turnout," Washington said in an interview last week. "I'm hoping for 975,000." Each voter above that number "will hurt," he said. Most veteran local election watchers think that more than 1 million of 1.3 million registered voters will turn out.

Don Rose, a reformist political organizer who masterminded Byrne's 1979 upset but who is sitting out this one, calls the black vote "the least racial in the city. They are split all over the place."

Washington's camp is hoping for boosts from weekend visits by Coretta Scott King, D.C. Mayor Marion Barry, Detroit Mayor Coleman Young, Gary, Ind., Mayor Richard Hatcher and former Texas representative Barbara Jordan. The appeal is to black unity at a time when whites have two candidates.

If Washington wins the primary, the Republican mayoral candidate, Bernard Epton, could become his party's strongest candidate for City Hall in many decades. The general election is in April.