If most Chicago residents have their way, acting mayor Eugene Sawyer may have trouble keeping his new job, according to a Chicago Tribune poll.

Sawyer, who is black, was elected acting mayor by the City Council following the death of Mayor Harold Washington on Nov. 25.

The poll of 650 registered voters found that 69 percent say the state Legislature should authorize a special election next spring. Current law requires an election to be held in the spring of 1989.

While white voters had a more favorable opinion of Sawyer than blacks did, most whites said they would choose someone else in the next city-wide election, the poll found. Only one-third of black voters interviewed had a positive image of Sawyer and just 40 percent said Sawyer would protect their interests.

Sawyer has not said whether he will run in a special election, but his chief opponent in the City Council election, Alderman Timothy Evans, has indicated that he probably will campaign for mayor. About 34 percent of those polled said they supported Sawyer's election as acting mayor, while 37 percent preferred Evans. Among blacks, only 10 percent said they wanted Sawyer elected acting mayor; 67 percent favored Evans.

About the only good news for Sawyer was that 86 percent of those surveyed said they are willing to give him a chance to see how he does.