The White House had been ready last month to propose major cuts in a program that helps states collect delinquent child-support payments from absent parents until high-level Republican women were able to convince officials to do just the opposite.

Transportation Secretary Elizabeth Hanford Dole and Health and Human Services Secretary Margaret M. Heckler urged that the administration's bill be modified, in part because they said they feared it would further erode President Reagan's support among women voters.

A congressional delegation of Republican women also opposed the bill during a White House meeting, and Rep. Barber B. Conable Jr. (R-N.Y.) expressed concern when the White House asked him to introduce it, according to a Conable aide.

Despite such resistance, the White House didn't decide to change its bill until July 12--two days before a House Ways and Means subcommittee had scheduled hearings on four other child-support enforcement measures. The administration's revised bill was put together so hurriedly that Conable introduced it before it was reviewed and approved by the Office of Management and Budget, officials said.

The dispute was over an OMB plan to "restructure" the federal Child Support Enforcement Program, a federal-state matching program created in 1975 to help collect delinquent child-support payments.

Non-payment of child support, mostly by fathers, has grown into a "national disgrace," Heckler said in an interview. Currently, about 8.4 million women are raising children whose fathers are absent. About 4 million of them have been awarded child support, Heckler said, but only 46.7 percent of them collect it. Twenty-five percent receive only partial payments and 28 percent receive nothing.

HHS said absent parents owed $9.9 billion in child support during fiscal 1982, but paid only $6 billion, cheating "women and children out of $4 billion."

"It offends my conscience," Heckler said, "that women and children are suffering because they are not being paid money rightly owed them."

HHS said the Child Support Enforcement Program helped recover $1.8 billion last year, but it still cost the government more than it saved in reduced welfare payments.

While each state runs its program differently, most states deduct a collection fee from the child support they collect for women and children who are not on welfare. But the fees rarely cover the cost of collecting the overdue child support and have the effect of punishing the recipients rather than the delinquent parent.

States also collect child support owed to families who are receiving Aid to Families with Dependent Children. In those cases, the state and federal governments use all the money they collect to offset the cost of the collection program and AFDC.

In fiscal 1982, the collection program cost the government $590 million. In return, the government recovered $180 million in fees and reduced welfare payments.

HHS also found that state collection records were erratic: six states had collected 88 percent of the funds, while the other 48 states and territories collected only 12 percent.

"OMB felt the government was underwriting a state program," an HHS official explained. "It wanted to develop an incentive for states and make the program more cost-effective."

In 1981, the administration cut back the government's contribution to the program from 75 to 70 percent. This year, it proposed replacing that with a federal match equal to the percentage of the AFDC payment each state picked up, or an average of about 54 percent.

States would be allowed to keep the money they collected from AFDC recipients only if it exceeded their administrative costs, OMB said. Finally, the OMB said states would be able to collect a bonus if they improved their collection rate for AFDC clients.

Dole and Heckler argued against the bill, in part because it would encourage states to concentrate on collecting child support for welfare mothers and ignore families who are above the poverty level. The states also complained because the proposal would switch a guaranteed matching program to one based on the amount they contributed to AFDC.

"OMB clearly was interested in using the collection program to reduce the cost of AFDC, not in collecting child support for mothers and children," a House subcommittee staffer said.

Under the revised administration bill, HHS would provide the states with 60 percent of the funds--still less than last year, however--and would not tie the funds to what percentage of the AFDC funds a state provides. Bonuses would be distributed based on how well a state collects child support for both welfare and non-welfare families.

A House subcommittee is expected to begin marking up the administration bill in mid-September.