“The law in my opinion is being abused now,” said Mr. Stuthman, who said he would push for a revision. “There are family services out there, but some people may lack the resources to take advantage of them, and we’ve got to take a hard look at what more we can provide.”

Todd A. Landry, the state director of children and family services, denied that the involved families had not had access to aid  most of the children, for example, were in the state Medicaid program and some had received psychiatric care  and he noted that well-publicized hot lines could direct families to help.

“Some parents had accessed our services but weren’t getting the results they wanted,” Mr. Landry said.

“The appropriate response is to reach out to family, friends and community resources,” he said. “What is not appropriate is just to say I’m tired of dealing with this and drop the child off at a hospital.”

Mr. Landry said parents and guardians were mistaken if they thought they could walk away from their responsibilities. For now, such children will be placed in foster care or with relatives, but the courts could require parents to attend counseling and might even order them to pay child support.

He said economic distress was a major issue in only one case, that of Gary Staton, 34, the father of 10 whose wife had died.

Mr. Staton, who gave up all but his oldest child, an 18-year-old girl, remains something of a mystery. His wife died in February 2007 after giving birth to the 10th child. Both parents had sporadic employment.