“My daughter told me this morning that she needed $9 for something at school, and I was like, ‘But I have to pay the rent,’” Ms. Hart said. “I gave it to her, and now I have to find that money someplace else.”

Barry A. Miller, the chief of the North Carolina child support office, said North Carolina, like about half of all states, passed no support money on to families. “We were seriously considering a change, but it’s doubtful we could do that now,” said Mr. Miller, who is also the president of the National Council of Child Support Directors. In North Carolina and elsewhere, lost federal aid may instead force cuts in personnel and enforcement.

On Nov. 15, 24 governors from both parties sent a letter to Congress asking it to repeal the cuts, arguing that they would hurt one of the government’s most cost-effective programs, which raises more than $4 in child support for every $1 spent on enforcement.

The intensified national effort over the last decade to establish paternity for babies born out of wedlock and to collect more support money, mainly from fathers, is often described as a great success. And indeed, collections have increased significantly, to some $24 billion in 2006 from $12 billion in 1996, helping many families avoid penury.

But for the poorest men and women, the story is mixed. Young fathers with little education or job prospects find themselves in arrears and facing jail time or the loss of their driver’s licenses as a result, making it all the harder to start earning and paying, said David J. Pate Jr., an assistant professor of social work at the University of Wisconsin, Milwaukee.

One startling indicator of how pervasively the poor are affected is highlighted by Daniel L. Hatcher, a legal expert on welfare issues at the University of Baltimore School of Law, in a forthcoming law review article. Of the nation’s total uncollected child-support arrears of $105 billion in 2006, Professor Hatcher writes, fully half was owed to the federal and state governments to recover welfare costs, rather than to families.

When Congress set up the current child support system in the 1970s, recovering welfare costs was an explicit goal, with some experts arguing that it was only fair for fathers to repay the government for sustaining their offspring and that giving families the money was a form of “double dipping.” But experience and research have suggested to most experts and state and federal officials from both parties that the policy is counterproductive — driving fathers into the underground economy and leaving families more dependent on aid.