THE number of families waiting to get into New York City's public housing - some 189,000 - is every bit as large as the number already there.That strong demand for what is usually considered housing of last resort is partly due to problems most cities share: growing numbers of low-income and homeless families and the lack of public-housing construction in the 1980s. In New York City's case, the location of projects in a wide array of neighborhoods, sturdy construction, and good management are also key. This city was a pioneer in experimental public housing in the 1920s and as recently as three years ago was rated tops among large cities in public housing management, according to a study conducted for the US Department of Housing and Urban Development (HUD). An unusually broad economic mix of residents is also a major factor in housing demand here. About 40 percent of New York City's public housing tenants are working families. Another third are elderly on fixed incomes. The proportion of welfare families, while higher than a decade ago, is an atypically low 28 percent. By contrast, some 80 percent of the residents in Chicago public housing rely on welfare. New York City Housing Authority (NYCHA) Chairwoman Laura Blackburne argues that many of the more than 300 projects here are actually oases of safety in troubled neighborhoods. "In many instances, public housing is the only thing that's working, that keeps the whole neighborhood from blowing apart," she insists. She points to a crime rate in public housing here only half that of the city as a whole. The homicide rate, however, is about the same as the city's. Mrs. Blackburne admits that the challenge is strong. A lawyer and civil rights activist who has been in her current job less than a year, she has made first-hand visits to check everything from outside lighting to garbage pickup. In February she accompanied law enforcement officials on a drug raid that led to 20 arrests and the breakup of two crack rings. "Of course it was dangerous, but every day I allow a drug dealer to function with impunity I am in effect putting my residents at risk," she says. In June she stood with Mayor David Dinkins at a Brooklyn project as he announced new emergency measures against illegal guns. Nearby gunfire interrupted his speech and dramatically underscored the point. In recent months the NYCHA has set up hot lines to receive anonymous tips on both drug dealing - calls go directly to the housing police - and illegal gun possession. Blackburne describes drug dealers as "two-legged roaches" whose first response to any obstacle is often violence. "These creeps aren't people who ought to be in a decent environment with decent people," she says, but illegal guns are more difficult than drugs to eradicate from public housing. Only about 30 guns have been turned in the six m onths since an amnesty on illegal weapons was announced, Involvement with drug activity or illegal guns is ample grounds for eviction in Blackburne's view. Under a new amendment to public housing leases, tenants must acknowledge that fact. She is not impressed by objections from civil libertarians. "Crime is not a civil right," she says. About 43 percent of some 600,000 tenants in New York City public housing are under 21, and crimes by and against them have dramatically increased. To keep young people more involved and busy, the NYCHA chairwoman has set up a new youth activities office that pulls in existing alternative high school and job training programs and adds a strong Girl and Boy Scout recruiting effort, a community service corps for older teens, and a voter registration drive. "Young people need to know they belong to something," says Blackburne, a mother of three. "It's just the nature of kids at a certain age. And if it's not something positive, it will be negative." New York City's public housing, which employs a staff of 15,000 (including 2,600 tenants), is a city within a city. Home ownership, an idea strongly supported by HUD Secretary Jack Kemp, "sounds fine if you say it fast," says Blackburne, but it requires some key prerequisites. She says she can help at a time when the city is cutting back on jobs by organizing small businesses to do needed repairs, from painting to plastering, that would offer tenants dependable jobs and shares that could eventually lead to firm ownership. "I call it 'job ownership, she says. "It's an idea that's a natural - long overdue," says Emanuel Tobier, chairman of the urban planning program at New York University's Robert F. Wagner Gradu- ate School of Public Service. Blackburne also intends to help in the continuing effort to move people up and out of projects and own their own homes by adding to needed affordable housing stock in ventures with the private sector. ve got to help build the housing these tenants graduate to," she says. SUCH efforts to improve and build new low-income housing around existing public housing are vital to the success of the whole process, insists William Kornbloom, a sociologist at the City University of New York Graduate School. He notes that the US has public housing for only 3.4 million of the estimated 30 million or more Americans now below the official poverty line. Any effort to increase home ownership, he says, must not be allowed to deplete the "incredibly paltry supply" of existing public housing stock. "You want to increase the pie - not diminish it," he says. "There is no low-income housing operation that has as many people trying to get into it as ours," comments Mrs. Blackburne. "It's the best thing going in wholesome, low-cost housing. The challenge is to keep it at that standard and create more of it."