Deborah Last was a little put out when her 8-year-old daughter told her class on career day that when she grew up she wanted to do "nothing," like her mother.

It was even worse when her husband, a D.C. police detective, told her recently she should get up in the middle of the night to care for their crying infant because "all you have to do tomorrow is baby-sit. I have a real job."

A family day care provider in Maryland, Last works 11 1/2 hours a day, five days a week, caring for as many as eight children in her home for a total salary of less than $300 a week. This is indeed a "real job," she said in an interview interrupted numerous times by the demands of several toddlers.

Home-based child care providers such as Last, often mothers of young children themselves, are taking on an increasingly important role in the daily care and early training of children in the Washington area and throughout the country as more mothers work outside the home.

But the providers say that parents and society as whole undervalue the role of a demanding job that, if done properly, involves teaching, nurturing and caring for a child's physical needs for most of his or her waking hours.

"It's amazing that parents don't want to pay $2 an hour for child care that lasts for 10 hours," commented Judy Griesse, a former elementary schoolteacher who has been a child care provider in Annandale for nine years. "They feel it's not something they should have to do . . . . Parents will pay whatever they have to for a cleaning woman. I don't understand that."

"The first thing parents ask is, 'What is the price?' " said Sher Ogden, until recently a teacher, who now cares for her own two infants and one other child in her home in Fairfax County for $100 a week. "I'll be going through my qualifications, and they will just want to know what it costs."

The answer to that question varies widely throughout the area, ranging from $35 a week per child to more than $100 a week, depending largely on the provider's neighborhood and the age of the child. And while parents may be surprised at how much this takes out of their weekly paychecks, providers are considered low paid by almost any standard.

The Children's Foundation estimates that more than 5 million children nationally, almost 70 percent of those in full-time day care, go to family day care providers. These generally are women who take up to six children into their homes, with little if any government regulation.

More organized than in the past, day care providers rankle at the term "baby sitter" and are trying to change their image to something more professional, complete with contracts, associations, conventions and child development training.

Ogden was among a dozen women who attended recent training sessions for providers held by the Fairfax County Office for Children, part of the county's recent efforts to attract and retain qualified day care providers. The office gets more than 1,000 calls a month from parents seeking child care, and even with a substantial increase in the number of registered providers over the past two years, there is demand for more, county officials said.

The county conducts a wide-ranging 40-hour course on child care for providers, along with workshops, such as one on "creative movement for cooped-up children" and one with the sardonic observation that "Parents Are People."

Providers, while acknowledging the numerous stresses on today's parents, have war stories about what they consider indifferent or thoughtless mothers and fathers, especially those who bring children with contagious diseases.

"One woman brought her child here with chicken pox and bronchitis," Last recalled in her home in St. Charles. "I called her at work, and she said she didn't want to take a day off to care for the child. The following week she took two days off because she had a toothache.

"Sometimes I don't know where the parents are. They may change jobs and not tell you," added Last, a mother of four and a child care provider for 18 years. In one incident, a little girl became ill and the mother had gone on a boat ride without letting Last know, she said.

And she had a parent who brought a schedule detailing what she should do with one baby during each 10-minute segment of the day, and another who did not believe that her child should be corrected for dumping plants on the floor.

After dealing with the stress of caring for a severely handicapped infant for 18 months, Last finally called it quits when the mother asked her to do it free one week.

Then, say numerous day care providers, there are the parents who show up late to pick up their child because they figure that the provider is at home anyway.

"Sometimes parents wouldn't even call and say they would be late. It's their child, but some just didn't care," said Michelle Crawford, a day care provider in Northeast Washington.

Crawford, who charges $45 a week per child, solved the problem by charging a $20 late fee for anyone arriving to pick up a child after her 6 p.m. quitting time. "Then they shaped up," said Crawford, who said she plans to open a day care center for about 20 children.

Despite the long hours and low pay, day care providers say there are many rewards in watching the children's progress and in managing a business.

"I love it. The kids all call me 'Mommy,' " said Mary Ellen Tasker, an Arlington day care provider who cares for five preschoolers. "I have good kids. They've all been through their biting stages and hitting stages."

Tasker, who charges $85 a week per child, quit her job as a bartender when she was unhappy with her son's day care provider. "If you can handle big people, you can handle little people," she concluded.

Judy Griesse, the Annandale provider, had wanted to start a preschool but found she has "the best of both worlds" by providing family day care in her home. "I could do what I wanted to do in terms of work, and I wouldn't have to be concerned about child care for my own children," she said.

Griesse and other experienced providers advise new providers to be businesslike, an attitude that sometimes surprises parents.

"Parents feel that because you are in a home, you will overlook certain things. New providers are surprised by that," Griesse said. The attitude of some parents, she said, is that "we're women, we're home. It's not really a job . . . . It takes an assertive woman to be in this business."

Local officials and experienced providers recommend contracts that specify hours and fees as well as the provider's policy on vacation and illness. Even then, some parents regard the contract as "almost a joke," and the contract can be difficult to enforce, Griesse warned.

Providers often include a specified amount of unpaid vacation, and on rare occasions paid vacation, in their contracts.

The field is still largely unregulated, with only minimal local requirements for people who want to care for up to six children in their homes. Even where there are licensing requirements, officials know there are many women who are caring for children and simply never comply. The Children's Foundation estimates that less than 10 percent of the family day care homes in the country are licensed or registered by a state agency.

The District requires that providers be licensed and have a home inspection, physical exam and written references. Maryland requires registration, involving a home inspection, physical exam, references and a criminal record check.

Virginia has no licensing requirements for care of up to five children in a private home. But Arlington has approval and licensing requirements, and all providers in Alexandria are supposed to be registered with the city.

Local jurisdictions keep lists of registered or licensed day care providers that parents can consult.

With parents often having a difficult time finding quality child care, local officials have launched campaigns to recruit more people to start day care services in their homes. A major effort was started by the Metropolitan Washington Council of Governments in October, and the number of registered or known providers rose from 1,295 in July 1985 to 2,232 in March this year.