RALEIGH, N.C.—Tiffoney Greene is racing a ticking clock. She has to meet job requirements by March 31, or the federal government will stop helping her buy food.

The same deadline looms around the U.S. as work requirements for nutritional assistance return in 22 states, including North Carolina, Florida and Washington. The federal rules limit Ms. Greene and other able-bodied adults without dependents to three months of food stamps in any three-year period—unless they work at least 80 hours a month, or meet education and training...