But others say the lack of cash support shows the safety net is torn. The main cash welfare program, Temporary Assistance for Needy Families, has scarcely expanded during the recession; the rolls are still down about 75 percent from their 1990s peak. A different program, unemployment insurance, has rapidly grown, but still omits nearly half the unemployed. Food stamps, easier to get, have become the safety net of last resort.

“The food-stamp program is being asked to do too much,” said James Weill, president of the Food Research and Action Center, a Washington advocacy group. “People need income support.”

Food stamps, officially the called Supplemental Nutrition Assistance Program, have taken on a greater role in the safety net for several reasons. Since the benefit buys only food, it draws less suspicion of abuse than cash aid and more political support. And the federal government pays for the whole benefit, giving states reason to maximize enrollment. States typically share in other programs’ costs.

The Times collected income data on food-stamp recipients in 31 states, which account for about 60 percent of the national caseload. On average, 18 percent listed cash income of zero in their most recent monthly filings. Projected over the entire caseload, that suggests six million people in households with no income. About 1.2 million are children.

The numbers have nearly tripled in Nevada over the past two years, doubled in Florida and New York, and grown nearly 90 percent in Minnesota and Utah. In Wayne County, Mich., which includes Detroit, one of every 25 residents reports an income of only food stamps. In Yakima County, Wash., the figure is about one of every 17.

Experts caution that these numbers are estimates. Recipients typically report a small rise in earnings just once every six months, so some people listed as jobless may have recently found some work. New York officials say their numbers include some households with earnings from illegal immigrants, who cannot get food stamps but sometimes live with relatives who do.

Image Kevin Zirulo shares a home in Lee County, Fla., with his brother and sister. They share a food stamp benefit of $300 a month. Credit... Stephen Crowley/The New York Times

Still, there is little doubt that millions of people are relying on incomes of food stamps alone, and their numbers are rapidly growing. “This is a reflection of the hardship that a lot of people in our state are facing; I think that is without question,” said Mr. Winstead, the Florida official.