WASHINGTON -- Critics of the watershed welfare law of 1996 forecast any number of problems, from starving children to dwindling benefits to Depression-era soup lines. But virtually no one imagined the strange new condition startling the experts coast to coast: States have more federal money, literally, than they know how to spend.

That is because the welfare rolls have dropped dramatically while federal financing remains, by law, fixed at historic highs.

Consider Wisconsin's version of the new welfare math. Five years ago, the state received about $317 million from the federal government -- or $4,100 for each family on the rolls. Last year, the state still got $317 million, even though its rolls had fallen more than 80 percent. That pushed the federal aid to nearly $22,000 per case, and with the rolls still shrinking this year it might grow to $35,000 per case -- a bit more than the cost of a year at Harvard.

Awash in federal dollars, the state has raised its welfare benefits 20 percent, created thousands of subsidized jobs, and offered poor women door-to-door rides to mandatory motivation classes. It has also used the money to bring new support to needy families outside the welfare rolls, as the federal law permits -- offering them child care, car loans, counselors, and annual cash bonuses of up to $1,600.

Still, Wisconsin had enough federal anti-poverty money left over to shift more than $100 million, through some creative accounting, into a tax cut for the decidedly nonpoor.

By contrast, Idaho and Wyoming have let their millions gather dust as their safety nets for the poor contract. Mississippi and Texas made modest increases in their notoriously low benefits.

This flood of federal dollars has created a rare, perhaps even unprecedented, moment of opportunity in programs for the poor. And it is almost wholly an unintended one -- a rich new financing stream for anti-poverty efforts created by the most conservative Congress in a generation.

Seeking to revamp welfare and restrain its costs, a newly Republican House and Senate reached a grand bargain three years ago with the nation's governors. The states got new flexibility to run welfare programs as they choose. In exchange, they accepted five years of flat federal financing. In the phrase of the time, the governors, predominantly Republicans themselves, promised to do more with less.

Instead, they wound up with more -- much more, on a per-case basis -- than anyone predicted, as a combination of a strong economy and tough new rules have pushed welfare rolls to stunning lows. Last year alone, federal payments to the states were $6 billion higher than they would have been under the old law, when falling caseloads meant smaller subsidies.

Now, in another twist, there is an intramural Republican dispute between congressional leaders who want to reduce the windfall and conservative governors who, protecting their budgets, find themselves in the unusual posture of championing welfare money.

On the ground, the new financing is altering anti-poverty assumptions in surprising ways. It has created the potential for new services in pockets of poverty long starved for cash and helped Florida find a prominent new place among the nation's innovators. It has left a startling financial imbalance across the Wisconsin-Illinois border, where welfare disputes have long raged. It has defined a new Western Mountain regionalism, from Idaho to New Mexico, where federal financing has brought new bounty but state services are notably few.

With vast new freedom to use the money as they see fit, states can intensify services for those left on welfare or extend a new hand to the working poor, buy drug treatment in the inner city or build bus lines to job-rich suburbs. But much of this opportunity is passing by unseized, according to an analysis of state spending records conducted by the New York Times. While some of the windfall has brought some new services, at times in the innovative ways predicted by the proponents of state control, nearly a quarter of the federal money awarded to date remains unspent.

That leaves a pool of idle anti-poverty money totaling more than $7 billion, a figure that current trends would push to $22 billion by 2002 when the welfare law expires. And billions more of the federal grants have merely replaced state spending, bringing no new benefits or services to the poor.

Of course, progress against poverty cannot be measured solely by the number of federal dollars spent. Some states have deliberately created reserves, exercising what they say is appropriate caution in case of economic downturns; others have squandered new opportunities through inertia and political infighting.

The Times analysis is based on the quarterly financial reports each state must file with the federal Department of Health and Human Services; interviews with state officials; and an in-depth look at three states with markedly different experiences. The financial reports cover state spending through the end of last year, the most recent time period available.

The analysis reveals:

On average, the federal government now awards states 64 percent more per family than it did five years ago, before the new law took effect. In 1994, the average federal subsidy per family was about $3,200 a year. Last year, with the same amount of money but far fewer people on the rolls, the average subsidy rose to nearly $5,300 a year.

While every state has seen its federal subsidy grow, the politically volatile disparities between the states have grown as well. That increases the likelihood of bitter new fights in 2002 when the current financing formula expires.

Much of the windfall has failed to translate into new benefits or services for the needy. Though federal subsidies for each family have risen by 64 percent, the rise in actual spending has been much more modest -- just 28 percent, when total spending is divided by the caseload.

The states slowest to spend the anti-poverty dollars include some of the neediest. By the end of last year, New Mexico, the poorest state, had spent just 69 percent of the money awarded to date. Mississippi and Louisiana, the next two poorest, spent 61 percent and 63 percent, respectively.