As winter's harshness grips the city, homeless people are on the move, pushing deeper into the city's cracks and crevices, to any alley and underpass that's safe and warm.

It's not just the cold that's driving them. It's also the New York City police.

Since a presumably homeless man smashed a brick into the head of a pedestrian in a random attack last month, police have been ordered by Mayor Rudolph W. Giuliani to roust the homeless and arrest them if they refuse to move on or accept a ride to a shelter.

But at the shelters, a set of proposed rules would make going there a Catch-22: Able-bodied shelter residents who refused to accept a job would be evicted, and if they happened to be parents, their children would be taken away on the grounds of negligence. This is what would have happened starting Dec. 13, but the state supreme court slapped a restraining order on the city this week. The proposed policy, said one judge, "strikes terror" in parents.

"I would call that policy Kafkaesque," said Maria Foscarinis, executive director of the National Law Center on Homelessness and Poverty. "You're being negligent because you're being kicked out on the street?"

Yes, says Giuliani's administration, which believes there is something wrong with an able-bodied parent who refuses to work, knowing it could lead to eviction.

Sparking a legal, political and ideological battle in which the traditional safety-net status of homeless shelters hangs in the balance, the city with the strongest constitutionally based right to shelter in the nation is attempting to implement the harshest sanctions against the homeless.

"The issue is whether or not the city has the legal right to put vulnerable children and families out of safety-net shelter and out on the streets of the city, particularly at a time when police have been directed to pick up homeless people from the streets and bring them back to shelters, under threat of arrest," said Steven Banks, who leads the homeless rights project for the New York Legal Aid Society.

Although critics accuse the city of "criminalizing" the homeless, Anthony Coles, a senior adviser to Giuliani, says the policies are intended "to move people who are homeless toward self-sufficiency and reduce the number of people in our city who are homeless."

"The best way of moving someone from poverty or homelessness is to help him develop a sense of personal responsibility," Coles said.

The notion that a lack of personal responsibility is a cause of a homeless person's problems is far from the truth, according to some experts who say that low wages and high rents are the real cause of homelessness.

The debate has become part of the ideological and political war that continuously roils between liberals and conservatives in this socially liberal and heavily Democratic city that has twice elected a moderately conservative Republican as mayor.

That clash has deepened with the onslaught of the political campaign season. Giuliani faces a formidable political challenge from first lady Hillary Rodham Clinton for the U.S. Senate seat they both are seeking. She has criticized Giuliani's homeless policies as "wrong." Giuliani--raising the specter of Clinton's "carpetbagger" status--has suggested that she doesn't understand the complexities of the problem because she is not from New York.

The homeless issue, though, is larger than a political campaign and has plagued this and many large cities for two decades. Nationwide, cities have taken increasingly punitive approaches to the homeless, with police crackdowns the rule rather than the exception. New York, with its outsize homeless problem, set that trend several years ago with Giuliani's policy of street sweeps as part of his quality-of-life focus to make the city safer and more attractive.

Those policies were generally popular. But a recent poll suggests that many New Yorkers now think the mayor has gone too far. A poll published earlier this week by the New York Daily News said 69 percent of respondents disapproved of arresting homeless people who refuse shelter, 54 percent disapproved of evicting people from shelters if they refuse to work, and 63 percent disapproved of putting homeless children in foster care because their parents refuse to work.

Nonetheless, the mayor is pressing forward.

Since the police crackdown on the homeless started Nov. 23, about 226 people have been arrested, 577 have been transported to shelters and more than 95 have been taken to hospitals, said Steven Fishner, Giuliani's criminal justice coordinator.

Defending his policies from critics who say it is simplistic to arrest the homeless, Giuliani and his advisers take pains to explain that arrest is a last resort and that attempts are made to channel homeless people toward services that are appropriate to their problems.

"What we're doing is, when we see a person laying on the street, we do not ignore that person," Giuliani told reporters this week. "We don't walk away and say let your problem get worse. The problem can be needing a place to live, needing a hospital, needing a shelter, or possibly it can be having to go to jail because you have a weapon or you committed robbery, burglary, trespass, public urination."

In the shelters, where on any given night there are about 24,000 people, the new policy on work is aimed at nudging people away from dependency and toward self-reliance. The threat of eviction and child removal is an incentive for an adult to accept a job that the city will provide.

"Asking people to work, making them work, is a very good thing to do for someone," Giuliani said during a recent news conference. "It's a very wise policy."

Coles said that a move toward a custody challenge against a non-working parent would only occur as a last resort and after other interventions had failed.

But human and legal rights activists are outraged at what they see as a push to erode the legal right to shelter that has been a safety net for the poorest of the city's poor. "The city's going to have to reconcile these policies before the courts," said Banks, who argued on behalf of the homeless and won the restraining order.

At issue is how the city will enforce state rules that require shelter residents to comply with all welfare reform rules, including getting a job. The issue has been argued in the courts over the past several years. In 1997, a judge approved the city's plans for shelter reform but barred it from using a parent's homelessness as a pretext for putting children in foster care. The city forged ahead with foster care nonetheless, arguing that it could be warranted on grounds of negligence. The issue will be argued in court Jan. 14.

The city's treatment of the homeless also is regulated by a broad consent decree dating to 1981 that stipulates that the city must provide shelter to people with physical, mental or social dysfunctions.

Up to 50 percent of the city's homeless show signs of mental illness, said Ray Brescia, director of the mental health project of the Urban Justice Center here. Nationwide, about 40 percent of the homeless appear to be mentally ill, according to a report released this week by the U.S. Department of Housing and Urban Development.

That study said that about 40 percent of the homeless are children and that their parents account for 30 percent of the adult homeless. Complicating their life prospects, 66 percent suffered chronic or infectious diseases, not including AIDS, and most lacked health insurance.

The HUD study said that homeless people's top priority is to get a job and that 44 percent of them had worked at least part time during the month before the survey was taken.

But even working full time, a minimum-wage earner cannot afford the fair market rent for an efficiency apartment in U.S. cities, according to a January study by the National Law Center on Homelessness and Poverty.

On the Streets

Here is a snapshot of homeless adults in the United States, from a Housing and Urban Development Department report released this week:

Parents

Without children 85%

With children 15%

Sex

Male 77%

Female 23%

Age

17-24 10%

25-54 81%

55+ 9%

Health problems

39% Mental illness

26% Drug abuse

38% Alcoholism

26% Acute infectious conditions (for example, bronchitis, pneumonia.)

8% Acute noninfectious conditions (for example, skin ulcers, lice.)

46% Chronic health problems (for example, arthritis, diabetes)