A group of House Republicans is backing a day-care bill that has the look of a legislative miracle.

It would provide $200 million to expand the availability of day care for needier families, possibly helping some of them to climb out of poverty, and it wouldn't cost the taxpayers anything -- or at any rate, not very much.

Rep. Nancy Johnson's proposal would work its magic by capping the income eligibility for the existing Dependent Care Tax Credit at $50,000, thus shifting the emphasis of federal child-care support from upper-income families toward those low- and moderate-income households that need it most.

Instead of providing government-run day-care centers, the Child Care Act of 1986, backed by the moderate Republican Wednesday Group, would provide federal vouchers to be administered by the states. Eligibility would be set at 200 percent of the poverty level. Denying eligibility to families earning $50,000 or more would save approximately $200 million a year in federal funds -- making the legislation essentially cost-free, while eliminating only about 8 percent of the current users of the tax credit.

"In light of fiscal constraints, we cannot continue to assist families with incomes well above the national average, while low-income mothers lack child-care resources so essential to their efforts to escape the cycle of poverty," said Johnson (R-Conn.).

Under current law, the richest households are eligible for the tax credits, while the poorest families earn too little to qualify for them.

That is one of the gaps the bill would address. The other involves the availability of child-care services. Under present law, federal child-care money is available to providers that meet state guidelines and to families that live near subsidized centers. "For the vast majority of low-income families struggling to maintain their independence and create a stable and secure family unit, there is no help at all," Johnson said.

She would cure that by requiring that states receiving voucher funds exempt home-based day care providers from state licensing requirements.

That provision is likely to spark some controversy, given the charges of child abuse that have been leveled against a number of day-care centers. But Johnson believes that licensure is no ensurance against abuse.

Moreover, since most children are cared for in "unlicensed 'underground' day-care homes, advertised by word of mouth," licensure has failed, she said.

"We initiated this project because the issue of child care has become increasingly important as women continue to play a major role in the work force," said Johnson. "In 1970, 32.2 percent of all women with children under age 6 were in the work force. By 1985 the figure reached 52.1 percent. Women, especially those in the low-income category, are often faced with the inability to find gainful employment due to lack of child-care options. This is a serious labor market problem and not just a women's issue."

There can be no question of its seriousness. The unavailability of affordable day care is one of the key reasons low-income mothers find it difficult to join the labor force. The supply of day care is so far behind the demand, according to the Wednesday Group, that there is an 18- to 24-month wait for subsidized facilities. Many children, including some pre-schoolers, are going without any day care at all.

If Nancy Johnson's bill can fix that, while expanding the choices available to low-income parents, and do it all without cost to the Treasury, she will have pulled off a most useful miracle.