Mayor Eugene Sawyer, lacking the monolithic support among fellow blacks that twice put Harold Washington in City Hall, bet his future on blacks voting in Tuesday's mayoral primary against front-runner Richard M. Daley.

"We must win this race," Sawyer told a crowd of blacks Monday night at his last campaign stop - a South Side church with Jesse Jackson. "I've got to do it for Harold."Daley, son of the quintessential political boss who ruled Chicago for more than two decades, remained confident in his quest for the Democratic nomination even though the most recent poll showed his lead reduced from 10 points to 7.

"From every community," Daley said in front of a Polish-American women's group, "you see some of the wealthiest people and some of the poorest people. You see them all reaching out to you."

Sawyer and Daley, the Cook County prosecutor, are the top candidates in a four-way race. The winner advances to the April 4 general election, which was forced by the death 15 months ago of Washington, Chicago's first black mayor.

Polls have indicated that Sawyer would get most of the black vote and Daley most of the white and Hispanic vote.

"I think the mayor's message has gotten through," said Sawyer's campaign spokesman, Larry Horist. "The black community has pretty much decided it's not right to abstain from voting, and they will turn out."

The nominee will face the winner of the Republican primary, whites Herbert Sohn or write-in candidate Edward Vrdolyak, and third-party candidate Timothy Evans, who is black, in April.

The winner of the general election will serve the final two years of Washington's four-year term.

Elsewhere, three challengers in St. Petersburg, Fla., are trying to unseat Mayor Robert Ulrich in a nonpartisan primary. And in Wichita, Kan., where residents approved a change in the structure of city government last November, 16 candidates are vying in the first mayoral election since 1916.

The Chicago campaign has been mostly devoid of the racial polarization that marred many previous campaigns. Yet Sawyer knows he must get some support from Evans' backers in order to block Daley and keep the seat he won during a raucous City Council meeting in December 1987, one week after Washington's death.