Nearly two years after the Reagan administration reduced the federal funds available to states for child-care services, it has begun a low-key campaign to encourage companies to help pay their employes' day-care expenses.

Margaret M. Hecker, secretary of the Department of Health and Human Services, and James Coyne, the top staffer of the White House's new Advisory Council on Private Sector Initiatives, have hit the road recently in support of the concept. Heckler has promoted the idea of day-care benefits with executives of high-technology and sporting goods firms in Portland, Ore.; of religious publications; of private hospitals and banks in Nashville, and of insurance companies in Hartford, Conn.

She has also instructed staffers in HHS's Administration for Children, Youth and Families to prepare brochures describing a variety of options for corporate support of child care, including referral services, child-care benefits for employes that firms may deduct from their income taxes and support for community day-care centers.

"We're trying to get away from the stereotype that support of day care means turning a third-floor abandoned storeroom into a romper room. Many chief executive officers just say, 'I'm not in the babysitting business.' We're trying to show there are other options," said Coyne, a former Republican congressman from Pennsylvania.

Heckler's cross-country jawboning, which started early this month, is the clearest indication yet of the administration's awakening interest in the child-care issue. In his State of the Union address last January, President Reagan told Congress that "a major effort will be focused on encouraging the expansion of private community child care."

Pointing to studies by consultant Dana Friedman, Coyne said, "This is a productivity issue for business. Amazing things happen at 3 o'oclock in the afternoon. Phone bills go up and productivity goes down because people are calling to see if their children have gotten home."

The Census Bureau reported last year that about half of American women over 16, some 44 million, work outside the home. In addition, the bureau said, 48.7 percent of the children of working women are cared for in day-care centers or by babysitters who are not related to the child.

The initiative has coincided with some administration efforts to improve Reagan's standing among women, who tend to support him less than men do. But there has been some skittishness within the administration about advocating day care vigorously, according to one administration official. Reagan has enjoyed strong support among advocates of traditional values, many of whom feel that women should stay home while their children are young.

In its first year, the administration reduced the funds available for social service grants to the states from $3.1 billion to $2.45 billion. The grants support services ranging from alcohol and drug abuse counseling to home-care services for the elderly to day care. Also eliminated was a provision that at least $200 million of the money be earmarked for day care.

Another casualty of the budget cuts was the Agriculture Department's day-care food program. Instead of providing three meals and two snacks a day to low-income children in day-care centers, the USDA now provides two meals and one snack.

However, the administration did support a congressional proposal to broaden the tax credits available for child care, which could cost the treasury more than $1.2 billion this year, according to day-care advocates.

Heckler's new push has been greeted with qualified enthusiasm from these advocates, who welcome any move to increase day-care options. They argue, however, that corporate support and tax credits tend to favor the middle class, while doing little for the lower-income working parents hardest hit by the cutbacks in federal social service funds.

"It's somewhat duplicitous to push child care in the private sector while cutting publicly funded child care, especially when low-income people have much less chance of getting child care in the work place," said Nancy Duff Campbell of the National Women's Law Center. Cutting Title XX the social services block grant and child-care nutrition and then to say that employers can make up the slack . . . is difficult to fathom."

The Children's Defense Fund, which is preparing a report on the effects of the cutbacks on state support for child care, has found that several states have narrowed eligibility standards, cutting off some low-income parents who work. "We are finding that more and more kids are being left alone," said the fund's Helen Blank. "We estimate that six or seven million kids under 13 are going without care for part of the day."

On the other side of the political spectrum, Phyllis Schlafly, the anti-Equal Rights Amendment activist and head of the conservative Eagle Forum, expressed skepticism for Heckler's crusade. "Justice would require that a company's benefits package not discriminate against a man supporting a wife who's taking care of her own children," Schlafly said.

However, while she said she that she believes "the great majority of working mothers solve their problems within the family or close friendship unit," she added, "I do feel it's the responsibility of the government to provide . . . for people for whom there are no other resources. You don't want kids left in the gutter."

"We're not trying to say there shouldn't be a lot of other partners in this enterprise," Coyne said. "We're just trying to push the private sector in this direction."