The experts call it "role overload." But to the average working parent, it's the constant juggling of work and home demands.

It's somehow nursing a sick child when you've already used every bit of sick leave. It's being late to a crucial job interview because the sitter didn't show. It's coping with a crying child on the phone just before your big presentation to the boss.

Whether you're like the senior V.P. at a Fortune 500 company who told her boss she had a flat tire when she really got to work three hours late because her child care fell through, or the cashier at a self-service gas station who hides her toddler behind the counter, researchers are acknowledging that the stress working parents deal with every day can be monumental. And that stress is apt to be heightened as schools recess for the summer.

At a recent conference here on "Parenting Issues of the '80s" sponsored by the Junior League of Washington, working parents surfaced as one of the hottest new concerns, not just for the increasing number of single parents and dual-career couples, but also for their employers. Despite tighter business budgets, the message was that corporate America is starting to care, and those companies pioneering in programs for working parents report that they pay off.

In addition, the White House is adding its clout. The Office of Private Sector Initiatives plans at least four pilot meetings with business leaders this month. The first, attended by about 35 executives, was held yesterday in Nashville; others will follow in Portland, Hartford and Kansas City.

If those sessions go well, 12 more are planned for the fall to consider the options of "crayons in the boardroom," says James K. Coyne, special assistant to the president for private sector initiatives.

"A small but growing number of employers in recent years have begun to recognize that if they ignore their employe's family needs, they will be ignoring the predominant concerns of an increasingly large portion of their work force," says New York consultant and White House private sector technical adviser Dana Friedman, who recently completed a national study for the Carnegie Corporation on "Employer Supports to Working Families."

(The Labor Department says two-income families now outnumber traditional single-breadwinner households by more than two to one and single parents head 20 percent of all families with children.)

Recent cuts in federal family-assistance programs, says Friedman, have created external pressures on corporations. Plus, trends toward fewer children (no older siblings to baby-sit) and less available extended families are forcing working parents to turn to their communities and employers for support.

"In Boston, more companies respond to family concerns at the work place than in any other U.S. city," says Friedman. Among reasons she cites: high-growth industries, Boston's concern for quality of life and even the types of managers it attracts from the city's colleges and universities.

"If there's an athletic facility, you can bet the C.E.O. chief executive officer is a jock," says Friedman, who found top management's personal style a crucial factor in their concerns about child care.

"The older company president, whose wife has never worked outside the home, has little concept of what balancing home and work can be like. On the other hand, young entrepreneurs may have a spouse in the work force and a preschooler in need of child care, so the issue touches him or her personally."

Houston, Minneapolis, San Francisco and Silicon Valley, Calif., also ranked high in child-care programs, as did service industries like hospitals and family-oriented businesses (General Mills, Gerber Foods, Stride Rite).

Friedman found, however, that those working parents most in need--whose home towns are hit hardest by recession, who are out of work or working for a small company--get the least help.

Friedman's study showed that only 600 companies out of the nation's 5 million businesses now offer some kind of child-care assistance. (Three hundred were hospitals and only 80 were on-site child-care centers.) But the number, she says, has "increased dramatically" over the last two years.

Simpler and cheaper corporate changes than on-site daycare may be even more effective to avoid "the daily collision between modern business and the contemporary family," suggests Marie Oser, founder, Texas Institute for Families, which has been helping families and companies work together since 1977.

"If I had to put my cards in only one place, I'd pick flexible sick-leave policies that allow employes to care for a sick child. It's the easiest and the cheapest and has the most to do with the parent-child relationship."

Oser, who headed the 1980 White House Conference for Children and Youth, the U.S. Commission of the International Year of the Child, and now also serves as a technical adviser to the White House private sector office, claims that sick children are the single biggest issue for every working parent, the one thing that "does them in."

Besides liberal sick leave, Oser proffers a full list of employe benefits to her corporate clients: financial assistance for public/private child care elsewhere, flextime, part-time and job sharing with partial benefits, adequate maternity/paternity leave, personal days, community information and referral, voluntary shift/relocation changes, broadened employe-assistance programs and work-place seminars on family well-being, time/stress management.

But the most important element is employer recognition of the employe's dual role, concludes Oser, a working mother of three.

"We are killing a bunch of people out there. And in our surveys, this is the way it comes out: husband, housework, kids. Every time. It's not what they want, but the reality is that peoples' lives bend to pressures. If the kid is clean and neat, okay, that is the issue. Never mind the emotional basket case. Never mind you are falling apart from too much guilt. Never mind the stress.

"We know from our data that the average parent of a preschool child sleeps 5-6 hours a night. They start their day between 5-5:30 in the morning and collapse at night. Self improvement? They don't even get to read the newspaper."

"Stress has become a national health concern, especially for working parents," agrees researcher/author Ellen Galinsky, project director, "Work and Family Life Study," Bank Street College of Education in New York. With initial support from the Ford Foundation, the 3 1/2-year international study will be the first to examine the interrelations among the family, community and the work place in various countries.

According to Galinsky, we may have a lot to learn from other countries on how to better mix work and private life. "The West Germans are out-stripping us yet they spend more money on vacations than any other nation and on Fridays, they always leave work at 1 p.m. And they never meet over lunch or breakfast as we do, they eat with their families."

"We need," says Galinsky, "to think about more part-time work and individually, about other aspects of our identity."

Galinsky, who has two children and leads seminars on working-parent issues for Exxon, advises parents to realize they can't do everything, to set priorities, to build in help and make time for themselves--whether it's taking an aerobics class or a bubble bath.

And she especially warns working parents to allow "transition" time to change from the faster, adult-centered day to the slower, child-centered time that follows. Many parents report "driving around" first before picking up their children. Others almost relish a long commute. One woman reports that she takes the last five minutes of every workday to "fade out." She clears her desk, unplugs the phone and just stares out the window.

Galinsky herself says it ain't easy. On those days when she comes home and everyone needs her at once and she doesn't even have her coat off yet, she says, "It helps to remember that I'm a pioneer."