E they Democrats or Republicans, all politicians love to chase deadbeat dads. With the White House, Congress and state legislatures all joining the hunt, the capture and extraction of money from AWOL fathers has become one of the most successful � and bipartisan � social policy crusades of recent years.

Collection of child support from the 11 million fathers who do not live with their children has nearly doubled in the past decade, to more than $18 billion a year.

"There is no way to escape these guys unless you get an alias and are prepared to hide for the rest of your life," said Damien Abeyta, 24, who lives in Denver and is the father of two infant sons from two mothers with whom he no longer has contact. The state of Colorado caught up with him last year, even though he was working an off- the-books construction job. It warned him that unless he acted at once to pay his arrears, his driver's license would be revoked.

Yet with the budget that President Bush sends this week to Congress, there is now bipartisan recognition at the highest level of government that the hunt for deadbeats is getting out of hand when it comes to the 2.5 million American fathers who are poor.

This is an unusual case of conservatives and liberals realizing that no-nonsense law enforcement is chasing some fathers away from their children. It comes at a time when both parties have agreed to support the crucial role that fathers play in child development.

The White House is acknowledging what recent social research has shown: for a poor absentee father and his even poorer children, the current system offers only family- unfriendly choices.

If a poor father pays child support to the state, it typically keeps the money to pay itself back for welfare benefits paid to his children. As a result, his children and their mother see no tangible evidence that the father is helping their lives. If he gives money to his family under the table, which greatly improves his relationship with the mother and often allows him more time with his children, it does nothing to reduce his legal child-support obligations. Instead, a father often finds himself living as an invisible man, working in the underground economy as his child-support arrears, with interest running at 12 percent in some states, mount ever higher.

The president's budget proposal will offer absentee fathers who are "dead broke" much better odds of seeing their children, while coming in from the cold of unpayable debt. The Bush proposal will include a provision to send all of a father's payments directly to his family. It will also propose spending $286 million over five years to reimburse states that pass child support on to families.

"What we are trying to do is set up family ties so that the father knows that the check is going to the family and the children, versus going to some government coffer somewhere," said a senior administration official, who spoke on the condition of anonymity.

Even those child-welfare experts who have almost nothing good to say about the Bush administration's policies toward the poor regard this proposal as innovative and much needed. "It is an important signal about the value of child support to low- income families and a message to poor fathers that if they pay support it will really make a difference to their children," said Paula Roberts, a lawyer who specializes in child support issues at the Center for Law and Social Policy in Washington.

There is only one state, Wisconsin, that passes along all child-support money to families without any reduction in welfare payments. Five years of research there suggests that the policy has been a solid success. It motivates fathers to pay more child support, encourages unmarried partners to establish paternity more quickly and shortens the amount of time that mothers stay on welfare.

It is no coincidence that Wisconsin's child support experiment, having been validated by research, is being proposed this year as federal policy under Tommy G. Thompson, the secretary of health and human services, who is a former governor of Wisconsin.

In the federal welfare reform law of 1996, which imposed a five-year limit on cash payments to mothers, all states were given the option of passing child support payments on to families. But none has done so with Wisconsin's zeal.

IN part, that's because of bureaucratic hunger for a large slice of the child- support pie. With 55,300 employees, the state and federal child-support system spends $1 of every $5 it collects on administrative overhead, according to federal figures. "The logic of the system overtook the policy, which was to help children," said Maria Cancian, an economist at the University of Wisconsin, who worked on an evaluation of the state's child-support reforms.

The federal and state enforcement system works well when collecting child support from middle-class dads with jobs, she said, "but the fathers of poor children are often themselves poor and the logic of forcing them to pay the cost of welfare is not compelling."

A piece of the welfare puzzle that is compelling to both Republicans and Democrats has emerged from a flood of research on poor families. It shows that a father's presence in the home is much more important to the emotional development of children than was previously understood. Among other things, it increases the odds that a child will complete high school, not take drugs and not become pregnant before the age of 18.

Complementing that research are findings in Wisconsin and elsewhere that a significant percentage of nonresident poor fathers (about one-third) have at least weekly contact with their children and that many would like to see them much more often. "When you are separated from your child, there is a part of you that dies every day," said Eric Legette, a nonresident father in Brooklyn who runs a program called Fathers With Voices, which offers men instruction in how to use the legal system to see their children.

The desire of men to be with their children is "the only carrot" that works with many poor fathers, said Robert Brady, head of the Young Fathers program in Denver. "These men may not care about the law, but they do want to see those kids," he said.

The Bush proposal to allow a poor dad's money to go directly to his offspring seems certain to lure more fathers in from the underground economy, child-support experts agree, while making the children and the mothers considerably happier to see them.