It is beginning to dawn on middle-class parents that the newly signed welfare reform law may increase the cost of child care for millions of American workers.

The Family Support Act of 1988 imposes new restrictions on child-care tax credits while offering improved benefits to poor people, many of them single mothers trying to work their way off welfare.In a sense, it's a trade-off. The unemployed get more help with child care. Parents already working may lose a benefit or two.

The new law makes it possible for welfare mothers to buy child care on a voucher or contract basis as well as for cash. It subsidizes child care while the mother is in school or in training. And it provides day care for a transitional year after the mother finds a job.

The other side of the coin is that, starting next year, the income tax credit for child-care expenses will be more restrictive than it has been in the past:

- Parents who set aside money for child care in a tax-deductible salary reduction plan no longer can claim a tax credit as well. Up to now, parents have been able to set aside up to $5,000 a year, then claim a credit for expenses in excess of that amount. The new law makes that nearly impossible.

- The child-care credit will not be available to parents once a child reaches age 13. Under the old law, the credit has been available until a child reaches 15.

- Parents claiming a child care credit must list the child's Social Security number on the tax return starting at age 2 instead of age 5. In some cases, divorced parents have been claiming the same child on both tax returns.

- Parents claiming a tax credit must list the name, address and Social Security number of the care giver. That makes it more risky for baby sitters to avoid paying taxes and could discourage parents from hiring illegal aliens.

The net effect of all this could be to make child care more expensive, even though parents still can claim a credit on expenses of up to $2,400 a year for one child and $4,800 for two or more.

If you earn less than $10,000 a year, you can claim a 30 percent credit, or a maximum of $1,440 a year. If you earn more than $28,000, you can claim a 20 percent credit, or a maximum of $960 a year.

But the new welfare law specifies that any money set aside in a salary reduction plan must be offset against the tax credit. Thus, if $2,400 is set aside to care for one child, or $4,800 for two, the tax credit is completely eliminated, according to Deborah Hrouda, a Washington benefits consultant.

Some parents may decide they'd rather give up the tax credit than expose the sitter to income taxes and possible deportation as an illegal alien. In any case, if the sitter hasn't been paying taxes and suddenly has to start, the child-care rates are likely to go up.

Helen Blank, director of child care for the Children's Defense Fund, says the changes are not "unreasonable," even though she would have preferred to keep the credit for children between 13 and 15.

Nor is there much reason to quarrel with the requirement that care givers should be identified, or that they should declare the money they earn on their income tax returns.

Much as it may disturb some cozy child-care arrangements, it's only logical that the people hired to watch the children of working parents should be paying taxes like anyone else.