In one department of the District government's Frank D. Reeves Municipal Center, the day can stretch for 11 hours, and the routine can be exhausting. Luckily, everyone has a comfortable cot and cozy cover for nap time.

In the Reeves Center at 2000 14th St. NW, in D.C. General Hospital at 19th Street and Massachusetts Avenue SE, and in the Department of Human Resources' Randall Center at First and I streets SW, the city offers its employes one of today's most coveted amenities: on-site day care.

"Their minds are at ease, because they don't have to worry about their children," said Barbara Ferguson Kamara, executive director of the city's Office of Early Childhood Development.

Mayor Marion Barry inaugurated the office a year ago in an effort to foster adequate day care in the private and public sectors. In February, the city adopted a law mandating day care in newly acquired or substantially renovated city government buildings if employes number more than 100 and collectively need care for 20 or more children.

The three facilities were operating or planned before the legislation, including the 18-child pioneer at Randall.

"It had become such a problem," said Aurelia Martin, Human Services' women's program manager. "When kids were out of school for a holiday, parents were bringing them to work . . . . Or they were calling all the time when they were left home. It can be a real distraction."

Accessible, affordable day care is vital at Human Services because of the staff's large female component and the desperation that can arise when single heads of households try to work, Martin said. One woman who called for help had three children under age 5, whom she left home alone during the day. When she became concerned for her children's safety, she left her job until the women's program found daytime care for them.

And, Martin said, "It's now happening to men." One employe, who had to drive his two sons to his mother's house in Maryland each day, then come to work in rush hour, "was getting docked for two hours every day" until Human Services helped place his children.

Unless the District makes an unexpected purchase or renovation, the first city building to fall under the D.C. Employees Child Care Facilities law will be Human Services' headquarters at Sixth and H streets NE, scheduled to open in late 1988 with space for more than 90 children. Already, women with children -- and some with child -- are calling Martin for reservations.

Because the law exempts hospitals and prisons, day care will not be mandatory at St. Elizabeths Hospital, which moves from federal to District control today.

But employes of D.C. General Hospital, where 70 percent of the 2,100 employes are women, desired day care so intensely that they raised $12,000 for the necessary renovation, according to Linda Ivey, employe development specialist and women's program manager. Employes held bake sales, discos and a baby contest among their children for the title of "Littlest General." Partisans paid $1 per vote, casting more than 4,000 ballots.

The center opened in June in Archibald Hall, a former nursing school on the hospital grounds. On the waiting list are "10 preschoolers, 15 infants . . . and we have three who are not yet born," Ivey said.

All entries in the 35-slot center must be children of D.C. government employes, with priority given to hospital workers. "We want to make sure we have it as a recruitment tool," Ivey said, noting that already it has helped lure a pharmacist and two nurses to hard-to-fill positions. Eventually, Ivey hopes to expand child care into nights and weekends.

All of the day care centers are run by private contractors, and Reeves and Randall accept children of nonemployes. The D.C. government offers subsidies based on family income and size, so the parents' cost per child ranges from nothing to $65 per week. For the fiscal year beginning today, the city has budgeted $17.2 million to subsidize the day care of more than 6,500 children in the District.

The city's Office on Aging, and its Corrections, Fire, Employment Services, Consumer and Regulatory Affairs and Recreation departments have asked the Office of Early Child Development to help them start on-site day care, Kamara said. But a Department of Administrative Services study showed that lack of adequate space will hinder openings in most locations.

Other public employers have recognized the need in the Washington area, which has the highest percentage of working women in the nation.

Fairfax and Arlington counties plan to begin employe child care early next year, with space for 75 and 65 children respectively. Montgomery County has 109 children in its employe child care center, and Prince George's has 70. Alexandria has a day care emergency plan for employes whose regular arrangements fail.

The federal government recently recognized on-site day care as a boon to employe morale, attendance and productivity, and announced a nationwide survey of its workers' needs.

The benefits are obvious, according to Debra Byrd, program director for the D.C. Parent Child Center, which operates the Reeves day care facility. Half of its 60 students are children of building employes.

"They're not under all of the stresses other parents are under," Byrd said. "They're more available in an emergency. They're upstairs."

"It's great to have her an elevator ride away," said Reginald Young-Bey, a paralegal specialist with the Office of Campaign Finance at the Reeves Center, whose daughter Alexis recently graduated from the 2- to the 3-year-old class.

Young-Bey, who lives across the city on 21st Street SE, formerly had a baby-sitter for Alexis.

"Here she's learning more, talking, saying her ABCs and singing," Young-Bey said. "I get serenaded on the way home."