With her husband, her two $48,000-a-year bodyguards, a small army of policemen and four cans of Raid, Mayor Jane M. Byrne set up housekeeping nearly two weeks ago in one of the nation's bloodiest and most wretched high-rise public housing projects.

Since the major and her City Hall muscle moved into the Cabrini-Green project, the most visible symptom of the hard life in a vertical ghetto, a three-month-long rampage of gang warfare and gunfire, resulting in 11 murders, at least 130 shootings, 120 stabbings and hundreds of rapes, robberies and assaults, has come to an abrupt end.

Street gangs, armed with rifles and sawed-off shotguns, no longer engage in all-night firefights. Competing gang leaders no longer dispatch 14-year-old assassins to murder their rivals.

There are cops -- narcoties agents, gang-crime specialists, vertical-patrol officers, special tactical unit patrolmen -- on seemingly every dreary corner of the project.

The calm in the combat zone has been credited to the plucky courage of the first-term mayor. Byrne's erratic administrative style has made her unpopular during her first two years in office, but a poll here last week showed that Chicogoans overwhelmingly approve of her move to Cbrini-Green and believe her motives are sincere.

While Byrne revels in her political birth, some local public housing managers, outside housing experts and even local police say they doubt that the mayorS mastery of political symbolism can substantially improve the lives of the approximately 15,000 poor people who are packed into Cabrini-Green, a monstrously ill-designed badland with 23 high-rise buildings and 55 row houses jammed in an area half the size of the Washington Mall.

Cabrini-Green, within seven blocks of the chandeliered condos and white-wine hauteur of Chicago's Gold Coast, resembles nothing so much as as a badly run, scandalously underfunded prison.

Open-air hallways in the 19-story high-rises are barricaded with iron grating and heavy-duty steel mesh. Stairwells reek of urine, stale beer and vomit. Garbage has backed up in trash chutes up to the ninth floor in some buildings.

Nearly every square foot of concrete in the hallways of the project, which was named after a saint and a labor leader, is covered with graffiti, much of which praises killing (such as Ken Killer Kool).

Each high-rise is labeled in spray paint with the insignia of the street gane -- the Black Gangster Disciples or the Cobra Stones -- which controls and terrorizes its residents.

Until police reclaimed Cabrini-Green in March, gangs had taken over the entire 19th floor of several buildings, smashing cinder-block walls and sniping from windows at passersby.

The gangs have had easy pickings in Cabrini-Green, because 70 percent of the residents are children or teenagers, and nearly 80 percent of the families in the projects are headed by single women on welfare.

In the past year, police say gang members have been extorting up to $30 a month from many welfare mothers. The gangs control virtually all narcoties and burglary operations in the project, extorting up to 50 percent of the profits of independent operators.

The presence of the mayor and more than 67 full-time police officers in Cabrini-Green has led to 360 arrests and the seizure of 41 guns. But police say that the narcotics and extortion business is continuing as usual.

"The gangs have no other choice but to wait out the mayor. They can't walk around here on the streets with guns anymore," said Lt. Sherwood Williams, in charge of the special tactical unit assigned to the project's own police station, which, because of frequent sniper fire, has steel shutters on its windows. "But we know that gang members are still making their rounds here and picking up money for the business they conduct without guns."

Tammy Taylor, 21, a welfare mother who lives with her two children in a $39-a-month apartment on the 10th floor of a Cabrini-Green building that has a reputation as a drug clearing house, says her life hasn't changed much since the mayor moved in.

"No nothin not to me. You know they slowed down the shootin'. But they are still out there. Lots of people still have to pay $25 a month to the Stones to get your [monthly welfare] check," says Taylor. She speaks hesitantly about the gangs, as does virtually everyone in the project. Although one of her friends says otherwise, Taylor claims that she has never had to pay extortion money to the gangs.

Taylor has a large scar on her shoulder and back from when her estranged husband accidentially shot her with a .357 magnum he'd bought for security. Like many young women in the project, Taylor carries a "pop-up" or switch-blade knife when she goes out at night.

"I say if the mayor didn't come here there would have been 'round about 25 dead so far," Taylor says. There has been one murder and one rape since the mayor's March 21 announcement that she was moving from her Gold Coast apartment to Cabrini-Green.

With or without the mayor of Chicago, Cabrini-Green manager Elton Barrett says that overcrowding and poor family discipline in the project will probably keep the garbage chutes jammed and many apartments filthy.

"We just have too many people," Barrett says.

Although the official population of Cabrini-Green is 13,626, police estimate that there may be as many as 7,000 additional "unauthorized persons" crowded into the 3,591 apartments.

Two days after she moved into her freshly painted one-bedroom apartment on the fourth floor of a notorious building police call the "Rock," Byrne called a news conference to announce that the solution to Cabrini-Green's problem is to "de-densify."

In St. Louis in mid-1970, housing officials at a similarly infamous and crime-ridden high-rise housing project had a similar idea. They decided to do something about the fundamental stupidity of stacking poor people in human filing cabinets, and dedensified with a vengenance. More and $36 million worth of public housing called Pruitt-Igoe was dynamited.

But the Chicago Housing Authority, which as an acute shortage of housing units and a waiting list of 13,598 families long, cannot afford that final solution at Cabrini-Green.

For nearly 12 years no new public housing has opened in Chicago, primarily because of a protracted federal lawsuit over the housing authority's penchant for building exclusively in black ghettos. The 2,223 housing units now under construction will not easy overcrowding significantly at Cabrini-Green or other city projects which house 125,000 residents.

The housing authority even has trouble kicking out or screening out troublemakers who participate in gang activities and tear up the buildings, according to Cabrini-Green manager Barrett.

Hamstrung by administrative procedures and court backlogs, it takes the authority up to two years to evict an "anti-social" family. Court decisions have forced the authority to accept virtually without screening, all applicants from the city's public housing waiting list.

"A family has to have an awful bad record, so bad, really bad, before we won't let them into Cabrini-Green, Barrett said.

On top of all these problems, the Chicago Housing Authority, like housing authorities in major cities such as Philadelphia, Atlanta, Newark and even Washington, is in danger of going broke.

Without an emergency bailout from the U.S. Department of Housing and Urban Development, the CHA says it will not be able to meet its April payroll. The authority has used up its entire $69 million 1981 federal subsidy, and Byrne says the CHA has a projected deficit this year of $80 million.

Five years of inadequate funding and recent budget cutbacks by the Reagan administration are creating a crisis for the 3.4 million people who live in the nation's public housing, according to a report issued last week by the National Association of Housing and Redevelopment Officials.

The report says that 32 public housing authorities, unable to pay their skyrocketing utility bills, are in danger of running out of money this year.

"Without a supplemental appropriation this year [which President Carter's last budget asked for but President Reagan's eliminated], some very large public housing authorities are going to turn belly up very soon," warns association executive director Robert Maffin. So far, the only major housing authority to go into receivership has been in Boston.

A House Appropriations subcommittee that listened last week to similar warnings of doom from housing authority officials has not made public its decision on a $100-million supplemental appropriation.

A HUD spokesman said the Reagan administration does not support the spending, and does not foresee major funding problems for public housing in the future. "It is our assumption there will be no shortfall," the spokesman said.

In Chicago, where Byrne has focused more attention on the problems of public housing than any public official in the city's history has, the fiesty mayor "is at the point now where she has got to deliver," according to her press secretary.

Last week Byrne announced a $1 million plan to hire off-duty police to patrol the project and initiate a test program to see if exterminators can head off the rats, roaches and assorted vermin that plague Cabrini-Green.

She has pledged to stay in Cabrini-Green until she can "change a word called despair to a word called hope," but she has not come up with any specific proposals that would reduce the number of children and single mothers in the project and, thereby, loosen the lock that street gangs have on life there.

She has, however, been hailed by friends and enemies as a master of the meaningful symbolic act. Byrne has managed to show concern for poor blacks in this highly segregated, 40 percent black city. At the same time, with her angry denunciation of a recently announced school busing plan, she's signaled to the white majority that she's not a liberal do-gooder.

Some housing experts in Chicago and elsewhere are pleading with the mayor to use her new-found political strength to go beyond short-term police crackdowns on troublemakers and give the housing authority power to enforce its rules about anti-social behavior and screen out undesirable families.

"Havoc in a building can start, in many cases, with just one vicious family," said John Washek, the court-appointed overseer of the bankrupt Boston Housing Authority. "One bad family can drive out 10, 20 or 30 families. One bad family can ruin a building. It has happened in Boston."

Cabrini-Green manager Barrett said, "I think we should be able to say to these people, 'Straighten up or step out.' Now we can say it, but it's almost impossible to make it stick." CAPTION: Picture 1, The Cabrini-Green project: 15,00 poor people packed into a monstrously ill-designed high-rise badland.; Pictures 2 and 3, Mayor Byrne and her husband Jay McMullen, sip coffee in their 4th-floor apartment, and walk to her limosine accompanied by two $48,000-a-year bodyguards. Photos by James DePree for The Washington Post