"They shouldn't be going through this," Ms Gates sighs. Somewhere in the shelter's day area, amongst the sagging furniture and plastic bags bulging with personal belongings of dozens of families, hides her third and eldest child: "I wish I'd known it was going to be like this before I had all these kids".
Less than a mile away, in the city's new YWCA, Fanesa Davis is enjoying a rare moment of calm in the basement computer laboratory. While her children play in the gleaming nursery a few steps down the corridor, Fanesa, 31, is scrolling through software on qualifying to become a plumber.
Neither woman - one desperate, the other full of hope - could have imagined even a few months ago that on this March morning these would be their circumstances. Black and husbandless, both belong to the huge class of American single mothers long sustained by a drip-feed of federal dollars from a six-decade-old programme known as Aid to Families with Dependent Children, AFDC. But that is all changing.
AFDC, for years the largest component of America's welfare system, is headed for extinction. Last August, President Bill Clinton signed a welfare reform Bill that ends guaranteed aid for single mothers and requires states to begin attaching job conditions and time-limits to assistance. Every recipient will have to work within two years of signing; no one will get the benefits for more than five years in a lifetime.
It is a social experiment of monumental proportions that has triggered anguish among some liberals, who foresee thousands being tossed onto the streets. Many European nations, Britain included, are eager to see the consequences, as they are also searching for ways to ease the welfare burden.
A view of the post-welfare picture is already emerging. Recent months have witnessed an astonishing decline in American welfare rolls. Caseloads across the country have plunged almost 18 per cent since 1994. The drop is explained partly by a strong economy and an unemployment rate of 5.4 per cent. Also at play, however, are reforms that many of the states had already started to implement before the change was endorsed by the President.
No state is further ahead than Wisconsin and no city more gripped by the changes than Milwaukee. A new welfare regime much tougher than that envisaged in Mr Clinton's Bill, will take effect in September.
Called W-2, it will instantly remove from the rolls all single mothers who fail to do some kind of work, whether full-time commercial employment, orjobs in sheltered state-run workshops.
A slightly less rigorous transition scheme called Pay for Performance is already in place, which also demands something in return for benefits. If they do not work, welfare recipients must attend subsidised job training courses or face deductions from their payments.
Wisconsin and its Republican Governor, Tommy Thompson, have been hailed for taming the welfare monster. Its "success" is posited on some extraordinary state statistics. In four years, AFDC rolls have been reduced by 41 per cent and they are still shrinking. The goal is to improve people's lives by ending their dependency on state assistance. But, with evidence of a rapid rise in the number of homeless in Milwaukee, is that happening? What is absent from the strategy is any attempt to track families once they leave the rolls.
Joy House has seen a 110-per-cent increase in bed occupancy in 12 months. Miliasia Gates believes her case reveals the new system's cruelty. Her February assistance cheque was slashed from $617 (pounds 385) to $212 (pounds 132) as punishment, she says, for missing one job-search class. Evicted from her apartment, she had no choice but to come here. "I feel like that instead of helping you off [welfare rolls], they hinder you, by cutting the money so much that you can't survive", she says.
Fanesa Davis, by contrast, is an example of what it is meant to happen. After six years on AFDC, she is dazzled by the possibilities opened up by her programme at the YWCA. "I have to be a role model to my kids," she says. "I don't want them looking at me and saying their mother's on welfare".
One of a handful of non-profit agencies contracted by the state to run job-training and job-search programmes, the YWCA is headed by Julie Taylor. "We know the opportunities are out there for them," she insists. "A big part of what we try to do is make people believe that they can make the changes; many people feel they don't have any power themselves to make the changes in their lives."
Study the reform laboratory that is Wisconsin and two encouraging factors become clear. Many of the keenest reform advocates, such as Ms Taylor, are not of a radical conservative ilk.
Their motivation is a desire to improve lives, not save state money. Secondly, Wisconsin, in its efforts to smooth the transition, expects in the short term to spend more money on supporting woman like Fanesa and Miliasia, not less. The additional funding will broaden healthcare insurance, for instance, and childcare subsidies.
The city's Democrat mayor, John Norquist, points out: "Going back to the old system of AFDC is not going to happen, because the electorate will no longer tolerate paying people for doing nothing."