To conservatives, the changes qualified as virtually a spiritual rebirth: faith in the power of work and not in what they viewed as a debilitating culture of dependence. To liberals, though, the new arrangement presaged misfortune. A leading liberal Democrat, Senator Edward M. Kennedy of Massachusetts, denounced the new law as “legislative child abuse.”

For a while, the Jeremiahs seemed to be losing the argument. Welfare rolls shrank, and then shrank some more. Having once approached 14 million, the number of people benefiting from TANF’s federal money and related state funds shriveled year by year, hovering around four million in 2015. In the first few years of TANF, hundreds of thousands of welfare mothers found jobs. Poverty rates declined. So did hunger among children. One year after signing the 1996 legislation, Mr. Clinton confidently told an audience that “it’s fair to say the debate is over — we now know that welfare reform works.”

But did it?

Things went swimmingly at first, principally because the American economy was humming in the late ’90s. The long haul told a different story. An economic slump at the start of the 21st century cost many of those newly employed mothers their jobs. Times got much rougher in the severe recession of 2007 and 2008. The safety net that TANF was supposed to provide began to look highly porous.

National poverty rates remain stubbornly high, staying in recent years at 15 percent. While initially effective in getting people off welfare, the system proved far less nimble at making them financially sound. Even when they found jobs, the wages tended to nudge them barely above the poverty line. And, all too often, they had a hard time staying employed when the economy soured. The poorest are usually ill prepared to flourish in a world where the technology and service industries are increasingly dominant.

Those federal block grants did not bring salvation, either. For starters, the annual total, $16.5 billion, has remained frozen for 20 years, meaning they are worth one-third less than they were in 1996. States may use the money as they wish, even if it means straying far from the original intent. Instead of becoming cash subsidies to destitute families or underwriting job-training programs, the grants are commonly used to finance college scholarships or child care arrangements — or simply to plug holes in state budgets.

Retro Report examines Arizona, where one in four children lives in poverty, one of the highest rates in the country. Arizona is also one of 14 states to have dispensed with the lifetime five-year eligibility limit. In July, it will be reduced to one year.

For Arizona officials, the temptation to divert federal dollars to purposes other than welfare proved “just too great,” said Jodi Liggett, a vice president of Planned Parenthood Arizona and a former senior policy adviser in the governor’s office. “There is this big, fat bag of money with TANF written on the outside of it,” Ms. Liggett told Retro Report.

Clarence H. Carter, a former director of Arizona’s Department of Economic Security, defended the diversion of funds. “They were used to support another important function of the safety net, and that’s strengthening families,” said Mr. Carter, who resigned last year amid controversy over how his agency had handled child abuse cases. “So the moneys were not hijacked.”

Nationwide, the Census Bureau counts 46.7 million Americans as living in poverty, which for a family of three (typically a mother and two children) means annual earnings of less than $20,160. About 20 million people live in deep poverty, with earnings below $10,000 a year for a family of three. In 2014, the last year with full census figures, the poverty rate among children — people under 18 — was 21 percent.

Plainly, government cash payments are not what they used to be. In 1996 they went to 68 percent of families with children that qualified as impoverished, according to the Center on Budget and Policy Priorities, a liberal research group in Washington. Now they go to 23 percent. In some states, the figure is minuscule: 8 percent in Arizona, 5 percent in Texas, 4 percent in Louisiana.

Other federal policies, like the earned-income tax credit and the child tax credit, offer some help. Nonetheless, millions of Americans get by on nothing besides disability payments or food stamps, formally called the Supplemental Nutrition Assistance Program. The social scientists Kathryn J. Edin and H. Luke Shaefer have calculated that 1.5 million American households subsist on no more than $2 per person a day.

Now some conservative lawmakers want to give control over food stamps to the states, just as was done with welfare. This time, they probably cannot count on an ally in Mr. Clinton, who acknowledges that ending welfare as we knew it was hardly synonymous with ending poverty as we knew it.

“It did far more good than harm,” Mr. Clinton said of the 1996 law in a speech two years ago. “But now, given the changed climate and the aftermath of the crash, the poorest welfare families, about 15 percent of the total, are worse off. And we should do something for them. And we ought to — all of us who supported it should — admit that.”

What that something might be is a “Back to the Future” issue for the next president and Congress to work out.

CLYDE HABERMAN, a regular contributor to Retro Report, has been a reporter, columnist and editorial writer for The New York Times, where he spent nearly 13 years based in Tokyo, Rome and Jerusalem. Subscribe to our newsletter here and follow us on Twitter @RetroReport.

This article first appeared in The New York Times.