In what was trumpeted as a major victory for women, the Reagan administration agreed to reconsider its budget cuts in a small but vital program: collecting unpaid child support from fathers who have ducked out on their families.

Some victory.

Formerly, the federal government paid 75 percent of the cost of collaring deadbeat dads, while the states paid 25 percent. This year the federal share dropped to 70 percent, and would have dropped to an average of 55 percent next year.

Instead--in a friendly salute to women--the administration kindly offered to hold the drop to 60 percent, down 10 percent from the present guarantee.

The president also proposed expanding the collection efforts--which is what makes headlines. But he doesn't propose to spend more money to make stepped-up collections possible.

A recent census report found that 8.4 million women nationwide had custody of their children in 1981, yet less than half had been awarded child support. Of those entitled to payments, only 47 percent received the full amount--an average of $40 a week. Another 25 percent got partial payments; 28 percent got nothing. The disinclination of many men to help support their children is one of the reasons that more women are falling into poverty.

For bleeding hearts, the growing feminization of poverty is of deep social and humanitarian concern. But it's also important to people who only bleed in the pocketbook. When dads don't pay, their families often end up on public welfare, supported by the taxpayers at large.

The states all have programs to try to collect child-support payments from delinquent fathers if the mother is on welfare. Some also help women who are not on welfare.

Automatic child-support collection is increasingly used if the father is within reach. Child support may be withheld from his wages, his income-tax returns and in some cases from his unemployment benefits.

When a family is on welfare, any child-support money collected from the father is used to reimburse the state and federal treasuries. The money collected for a non-welfare mother goes directly to her, for the benefit of the children.

In recent years, Washington has been discouraging child-support collections for nonwelfare mothers, because the goverment didn't get anything back for its efforts. The idea has been to use the program for the benefit of the federal treasury, not for the benefit of women and children.

Several bills now before the House Ways and Means Committee would strengthen the collection efforts, especially on behalf of nonwelfare mothers.

Rep. Marge Roukema (R-N.J.) wants to make child-support payments automatic, by withholding them from the father's wages right from the start. Rep. Carroll Campbell (R-S.C.) would report delinquent dads to credit agencies and put liens against their property.

Rep. Barbara Kennelly (D-Conn.) favors wage withholding after two months of arrears. She would also extend to nonwelfare mothers the current, and highly effective, collection system used for welfare mothers: deducting overdue child support from federal income-tax refunds.

The major bill is the administration's new proposal brought forth in good part through the efforts of Republican women politicians. Roukema told my associate, Wendy Cooper, that the argument that caught the president's attention was the need to end the present discrimination against nonwelfare mothers.

The administration now proposes to pay bonuses to the states for improving collections for both welfare and nonwelfare mothers--the bonuses making up for the cut in guaranteed funding. It may also seize the federal tax refunds of delinquent fathers of nonwelfare families--a change in attitude welcomed by state directors of child-support enforcement.

But Dan Copeland, head of the State Directors Association, worries about the cut in guaranteed funding. State legislators may be willing to replace lost federal money, but many child-support programs depend on county budgets for support.

"When the county commissioners see a cut in the federal guarantee, they respond by reducing their own efforts," he says.

Extending the child-support enforcement program to cover more nonwelfare mothers is a fine idea, but it's a hollow gesture if the president doesn't provide any money to do the job.