Like Mr. Constance. “I couldn’t really find any kind of work or the help that I needed to help raise my son,” said Mr. Constance, 53, who until recently had been living at a homeless shelter in New Orleans with his 9-year old son, Pablo.

A prison record from the 1980s, the result of selling two ounces of marijuana in Texas, has hampered his search for work as a house painter. “That’s why I say it’s been a hard road for me trying to raise my son, with all those ghosts and shadows over my head,” he said.

As he discovered, benefits vary greatly from one state to the next. He applied to the Temporary Assistance program in Miami, he said, but was uncertain about why he never received any. “It wasn’t nothing but problem after problem after problem,” he said.

Last year, he moved with his son to New Orleans, where he said he was offered $123 a month in Temporary Assistance for Needy Families aid in exchange for community service. He tried it, but the time and money spent commuting wasn’t worth it, he said, explaining that he was better off using the time to look for an odd job, a car to wash or a yard to rake.

He said he received $318 a month in food stamps, and that his son received $390 a month from disability payments through his mother, who still lives in Florida.

After months of bouncing around in emergency homeless shelters, the two are now settled in an apartment. The $700 monthly rent is being paid by the Salvation Army for six months, while Mr. Constance searches for a permanent job. “With the light bill and water bill, I don’t have enough to take care of all of that,” he said.