A frisky April breeze billows through the apartment's loosely woven beige curtains, bringing with it rush-hour fumes from a No. 70 Division Street bus and ruffling the blond hair of the most celebrated resident of the city's most crime-riddled public housing project.

Standing in the glaring white kitchen of Apartment 402 of the Chicago Housing Authority's headache known as Cabrini-Green, Mayor Jane M. Byrne is pouring her husband a cup of coffee.

Jay McMullen, her husband and political adviser, is sitting at the table eating a sweet roll. "It ain't the Ritz, but we'll get by. I've slept in worse places. It doesn't really matter as long as I've got a mattress. Do we have any juice, dear?" McMullen asks as his wife settles into her chair.

"You want some V8?" the mayor responds as she starts for the refrigerator, then stops, turns and looks at her husband. "Forget it," she laughs and returns to her chair. So much for domesticity.

A short time later, on that Chicago spring day late last week, 100 members of the press were invited up for coffee and a tour of what the mayor calls her "city home," a two-bedroom apartment that for three days had been Jane Byrne's part-time residence and a temporary bromide for her tumultuous political career.

Yesterday, at a business awards dinner, Byrne announced her candidacy for reelection in 1983, surprising her audience with the timing but not the intent. rAlso yesterday, she said she will disclose detailed plans late this week for heightened security measures at the housing project.

After that, she said that she and her husband will visit there only occasionally while living in their own luxury highrise in downtown Chicago.

"We will put into effect everything we're going to put into effect and then we'll watch it," she said. "Should there be any more trouble, it's five minutes in the car."

Meanwhile, she is hosting kaffee-flatsches for Cabrini residents, eating dinner at the local fire station and writing a diary of her experiences for the Chicago Sun-Times. In a recent edition, Byrne suggested her stay in the project was sort of an adventure for her and McMullen.

"Jay always wanted to live in a romantic cold-water, walk-up flat on the Left Bank in Paris," she wrote. "I told him last night he finally made it -- Chicago style."

As the midpoint of Byrne's four-year term approaches, political observers agree that almost every positive accomplishment of her administration has been overshadowed by political gaffes, her often-combative attitude or an ill-timed remark.

Some of the Byrne-isms that have brought her national attention include: throwing a Mississippi-riverboat-style gala for Jimmy Carter and then abruptly switching her support in the presidential campaign to Ted Kennedy; donning sunglasses and a black fedora and striking a pose with Blues Brothers John Belushi and Dan Aykroyd (the picture wound up in People magazine); opposing the son of her late mentor Richard J. Daley in November's race for Cook County state's attorney (Richard M. Daley won anyway).

A telephone poll taken in December for the Chicago Tribune found that only 3 percent of Chicagoans felt the mayor was doing an excellent job. Forty-six percent said they thought Byrne was doing a poor job.

Shortly after that poll was taken, a string of killings began at Cabrini-Green, the 70-acre wasteland of dull brick highrise and lowrise apartments that serves as a last resort for Chicago's working and unemployed poor. By last week, 11 people had been shot to death and 37 injured in what police say is an outbreak of street-dang violence at the project named for Mother Frances Cabrini, the first American saint, and William Green, successor to Samuel Gompers as head of the American Federation of Labor.

On a Saturday night two weeks ago, before the 11th victim had died, Jay McMullen announced that the city's first couple would be moving into Cabrini-Green to get a firsthand look at crime in the complex and to "study the life style" at Cabrini, one mile from elegant Michigan Avenue.

McMullen's announcement touched off what Chicago Sun-Times gossip columnist Irv Kupcinet called "the media event of the year." An editorial in the usually staid Tribune said Byrne's "unpredictable behavior has hit a jackpot." The Sun-Times allowed as how Byrne's decision was "clever politics" but called it "bold and gutsy" nonetheless.

McMullen, a former City hall reporter for the now-defunct Chicago Daily News, bristles at the suggestion that the mayor's move into Cabrini is a publicity stunt. "Anybody who thinks it is can move into the apartment next door and share the politics," he says.

Many Cabrini residents are not so sure Byrne's presence will make a difference. "What's going to happen is going to happen anyway while she's asleep," resident Roberta Jones says. Second-graders from the project wrote the mayor letters, warning her of the perils of life at Cabrini. "It's dangerous for you to go in Cabini green projects," Yalking Burnett wrote. "You may be shot stab or assassinated or killed. You shouldn't go in the black neighborhood. I think that is very crazy. See you at the funeral Jane Byrne."

Seemingly undaunted, Byrne and McMullen last week moved into a corner apartment at 1160 N. Sedgwick. McMullen brought four cans of Raid. Byrne brought her bodyguards, who moved into the apartment next door. The mayor told a television interview a few days ago that she is so well-protected in her apartment that she is "prepared for anything up to a nuclear war."

Apartment 402 hardly resembles a bunker.

The housing authority painted the cinderblock walls mustard yellow and apple green and Montgomery Ward furnished the two-bedroom unit down to the off-white ironstone plates, the gold-colored glasses, the smoke detectors and the color television set -- for free.

The apartment looks like a furniture store showroom, with its basic mushroom color scheme and its perfectly placed throw pillows. The decor lies somewhere in that bland nether-world between sophisticated and tacky. Cane-backed dining room chairs with cut-velvet cushions. A bedroom done in catalogue Chippendale. Pictures of large-eyed cats hanging on the walls.

Outisde 402's front door is a different story. Outside, it looks like public housing. The halls of Byrne's building are red brick and concrete. Bare light bulbs dimly illuminate the narrow, angular halls. Iron mesh floor-to-ceiling fencing has been placed between open-air sections of the hallways, giving the appearance of a prison catwalk. The halls smell of disinfectant.

On Byrne's floor, the graffiti has been scrubbed off the bricks. The second night she spent there, someone set the garbage in the garbage chute on fire. It had been backed up nine stories high. Over the weekend, the mayor emerged victorious in a battle with two roaches on her apartment's floor.

Fearing snipers, the police have warned Byrne to stay away from the windows, but if she were to look to the east, she could see the luxury highrise, only seven blocks away, where she and McMullen maintain their "real" home. She says she plans to keep the Cabrini apartment, for which she is paying no rent, until the end of her term.