A COUPLE OF WEEKS AGO a group of parents, children and infant-day-care providers went to the District Building to protest Mayor Marion Barry's plan to end day care for infants at four centers in the city and to put them, instead, in private homes. When you stack this money-saving proposal up against Barry's plan to fire 150 jail guards, it's small potatoes. But to the mothers involved, the kind of day care their children get while they work or learn a skill is pretty important. And for once, they were able to find a city official who understood that and who did something about it.

The city's Department of Human Services currently subsidizes day care for 91 infants whose mothers are in training or working. Without the day care, most if not all of the women would have to stay home to care for their babies, which means they would be going on welfare. Barry's proposal, which initially was supposed to save the city $175,000, would have subsidized care for these infants in family homes, which are licensed by the city but which the mothers feel offer a less stimulating and enriching atmosphere than is provided at well-eqiupped centers where there are other children. Some mothers said, quite simply, they would stay home rather than send their babies to a day-care situation they consider to be inferior.

Rudolph Hutchison, administrative officer of the Catholic Charities Model Cities center, which provides care for 21 babies, says he talked to officials in the Department of Human Services and in the mayor's office. "My question was is this decision irrevocable, and they said yes. At that point, I said we have nothing to lose." He said eight carloads of people went to the District Building to plead their case in the City Council chambers. Audrey Rowe, head of the social rehabilitation administration of DHS, showed up to state the city's case.

"Our position was we understand there had to be money made up," says Hutchison. "That was not an issue with us. What was an issue was that we didn't feel we were consulted concerning ways it could be saved."

"We said there were some alternatives the department could look at and we could show them how they could save 91 children and save the money, too. At that point, Miss Rowe said, if you can show us that, then we can bargain."

A half hour later, the group met with Rowe in her office and proposed several pretty straightforward ideas for saving money. For example, a law went into effect last year providing a sliding scale of fees for parents who use the centers. A suggestion that was ultimately adopted was that those fees actually be collected. Rowe and a representative of the infant-day-care providers spent the next week going over projected costs of day care, actual costs, and how the centers could save money. They found, among other things, that the projected costs were vastly more than the actual costs, but in the haste in which the mayor's budget cuts were thrown together the figures were never examined closely.

"Miss Rowe's position was the key," says Hutchison. "She was willing to sit down and take the extra week to work it out." Hutchison, who has been involved with day care since 1972, said this episode "is the first time that I can remember dealing with the Department of Human Services where they have been willing to sit down after they made a decision." "I can think back to the Joe Yeldell days. He would have said to hell with it. That's my decision and if you don't like it you know what you can do with it. Miss Rowe said meet me in my office in a half hour and we can talk."

The infant-day-care program has been saved, at least until September, when a new budget cycle goes into effect. What will happen then is anybody's guess. You cannot count on finding substantial over projections in costs. But the day-care providers at least can make the kind of pitch that people who make up municipal budgets understand -- or at least they ought to.

Jan Calderon Yocum, executive director of the Day Care and Child Development Council of America, says they often don't. "One of our biggest problems, whether it's infant day care or not, is the whoe lack of understanding of the fact that day care is a supportive system which families who are in the labor force need to become an economically stable unit and that in turn makes the city or the county stable because the taxes the parents pay far exceed what it costs to provide day care. When that supportive system is cut off you have communities as well as families operating at a deficit. How many of those families will go on Aid to Families with Dependent Children? How many of those children will go unattended because their parents work, which goes to delinquency.

"Detroit determined that 25 percent of their home fires were caused by children who were left unattended. If you take the money it costs to send out the fire department, the fire insurance, the damage to property and life, that far exceeds what it costs to provide day care.

"Many times, in cutting budgets, the providers and the consumers themselves are never asked for ideas as to how it can be done," says Yocum. Here, she says, the day-care lobby found someone who would listen to them and who did not try to play off the infant-care lobby against the people who need and provide care for older children.

Loise Sulliivan, executive director of the Rosemount Center, which provides care for 28 infants, was another person who came away from the episode impressed. "Audrey Rowe came to terms with the reality of the budget but she also came to terms with the reality of the human beings involved. She was responsive. She saw us right away. She saw us several times. She knew it was a crisis.

"She really cared. I just thought it was a whole new era of working together," Sullivan says.

That's the kind of city official that makes you think that for all the budget crisis we keep hearing about, this is a city that could work.