Gerald Williams, a caretaker at the National Institutes of Health, took time from his lunch hour recently to watch his daughter Emphris and some other 3- and 4-year-olds dip Easter eggs - and fingers - in colored dye. He didn't have to go far - they were at a day care center on the NIH grounds.

"It would be a terrible thing to see it end," he said of the parent-operated, nonprofit day care center. Williams reports to work every day at 8 a.m. after a 45-minute drive from his Arlington home and works as much overtime as he can get. His wife is a stenographer at a nearby Army facility. He says alternative day care centers open too late for them.

But now a government economy move is threatening the future of the NIH day care center and others like it.

Emphris is one of about 350 children in the Washington area attending such centers at various federal agencies - bureaucratic cases where the only papers being shuffled wild finger paintings and craft drawings, and where the [WORD ILLEGIBLE] lights are dimmed at midday.

Parents can have an occasional lunch with their children and they [WORD ILLEGIBLE] close in case of a medical emergency.

Lately the centers' air of innocence hustled and bustle has cloaked an undercurrent of anxiety among parents and others.

President Carter's budget management are proposingto start rents at the going rate for the space occupied by day care centers and certain other "nonfederal activities." The agencies are now allowed the option of providing the so-called excess space rent free, or at reduced rates.

The additional cost of the rent would price the program out of the reach of many parents, officials say.

With a number of officials, women's organizations and other interest groups, as well as parents, opposing the proposed change, the issue promises a showdown. On the one hand is Carter's avowed support for the family and increased job opportunities for women and minorities and on the other, his determination to tighten the federal budget.

"Because the potential disruption is of such magnitude," the government has decided to hold a public hearing May 9, according to an official of the Office of Management and Budget (OMB).

Opponents of the plan maintain that the resulting higher day care costs will hit hardest those who need the centers most - low-income parents, single parents, some of whom can't work without such facilities.

They say also that it will have a chilling effect on the government's continuing efforts to promote on-site day care centers in private industry as well as in its agencies.

Joseph A. Califano Jr., secretary of Health, Education and Welfare, is opposing the OMB plan, and Margery Waxman Smith, executive director of the Federal Trade Commission, has said the plan will have "disastrous effect on many working routines in the federal service."

"We would have to go out of business," said Virginia Burke, coordinator of child care at NIH. That center, already operating at a deficit of about $150 a week (made up from parents' doughnut sales and other sources), is housed rent-free in an otherwise unused half of a cafeteria building.

A parent such as Gerald Williams, who now pays about $43 a week for the child care (teachers, equipment, meals and the like), would find it difficult to pay twice that amount, which is what the fee would be if NIH is forced to start charging standard rent for the space, Burke said. The added rental cost is estimated as much as $35,000 a year.

Opponents of the OMB plan also contend that OMB is treating day care center's more harshly than other, comparable employe service activities using federal space - such as parking facilites (which it does not mention) and employe recreation associations.

Officials of OMB maintain that the rent-free space for day care centers amounts to a taxpayer subsidy for facilities that are not available even to all federal employes.

The centers have been "growing like Topsy" in federal buildings around the country and officials have no figures on how many there are, according to Lester Fettig, director of OMB's office of federal procurement policy."So you can see that a minimum, someone had to say something sensible about how to treat them."

Fettig's office wants to establish a uniform policy on these and other uses of federal space for nonfederal activities - a policy which will cut government costs for office space and in some cases the electricity, maintenance and other support services which go with it. This is a project first recommended in 1974 by the Government Accounting Office, which monitors other agencies' financial practices.

"It's a matter of management discipline," Fettig said. "Considerable sums are involved." He added, however, that he wished the thorny issue were not in his lap.

One center located in an HEW building (part of a research demonstration project for the agency) has cost $226,000 in remodeling and repairs, according to OMB figures, and its 2,190 square feet cost HEW a rental payment of $20,550 a year.

Based on the costs of this facility and two others - one in another HEW building and a new one at the Department of Housing and Urban Development - OMB estimates the cost to alter federal space for child care purposes in downtown areas is about $3,660 per child. The costs to be passed on to the parents under the new plan would result in an increase in fees of about $14 per week, they estimate.

But some day care facilities have not had such extensive remodeling, administrators pointed out.

OMB notes also that the District of Columbia has more than 286 licensed day care centers and 500 day care homes in privately-owned or other nonfederal space.

These outside centers don't suit everyone's needs, however, as parent Julie Carvalho, an employe in HEW's office of civil rights, observed.

"A major problem is that a lot of them close too early. A lot of the ones in (the suburbs) close at 6 and most people here don't get off until 5:30. If you have a long drive, you aren't going to make it."

Another advantages to on-site facilities, she said, is "if you have to work late, you can just go (to the day care center) and bring your child to the office to play until you can go home."

Proponents of on-site child care maintain that costs are offset by other considerations, not merely convenience and economy for parents but for their effect on employe morale, efficiency and attendance, and on family togetherness.

Many parents have "regular Tuesday or Thursday lunch appointments" with their children, noted Marion Green, director of the NIH center. "When their child has a birthday party, they can take two hours' annual leave and come on over."

The on-site center is "good for my nerves," said Ernestine Gregory of Silver Spring, a lab technician at NIH. On a salary of about $14,500, she is the sole support of her granddaughter Sadrea, 4, whose mother was killed in an accident. She, too, mentions schedule problems with outside day care centers and "long drives through traffic" to pick the child up.

"One of the values of this center is the heterogeneous quality of the children," Green said. They come from all government income levels and a variety of ethnic and national backgrounds.

This mix is made possible in part by the center's sliding fee scale - from $10.50 a week to for low-income families to about $55 a week for the more affluent.

Not all the centers are able to provide such a scale, but rather charge the same fee for all income levels. The mix of families generally is dominated by low-to middle-income people, (GS5s, 6s and 7s) according to Ruth Nadel, coordinator of the Department of Labor's Alliance for Child Care in Federal Agencies.

Under the OMB plan, some other employe service operations could continue to get rent-free (or reduced) government space. Employe credit unions, vending facilities operated by blind people, veterans services and other categories of users are exempted from rent charges by various statutes, OMB officials said.

OMB also is allowing employe recreation and welfare associations the right to free space, though no statute requires it, as "encouragement to the voluntary efforts of employes."

The recreation groups do not require space reserved solely for their use, as the child care centers do, OMB officials said.

Of the failure to mention the parking question, Charles Clark, an OMB administrator who has been involved with the space-rental issue for several years, said "I guess that's a Senate problem, one we aren't ready to deal with yet."