At the same time, a number of cities, including Chicago and Flint, Mich., considered drug testing public housing residents. There have also been proposals in Congress for nationwide testing of welfare recipients.

To date, most of the proposals have failed to win support because of concerns about legality, stemming from a decade-old federal court ruling. That ruling struck down a Michigan law that mandated testing for all welfare recipients as a violation of the constitutional protection against unreasonable search and seizure.

Money has also been an issue — the sides dispute whether the savings in unpaid benefits will eclipse the spending on administration, including the cost of testing.

“It really speaks to how the politics of the moment are dominating the policy conversation in the virtual absence of any evidence,” said Harold Pollack, a professor at the University of Chicago whose research has indicated that people on welfare used drugs at rates similar to the general population.

In Arizona, under a 2009 program reauthorized this year, applicants are tested if they answer yes to a question about recent drug use. Only 16 out of 64,000 answered yes; 931 did not submit the form. The state estimated the savings on benefits had totaled $116,000.

The law in Florida, where the average recipient receives $253 a month for less than five months, is more expansive. It requires applicants to pay for their own drug tests, which the state says costs up to $40, and the state will reimburse those who pass. People who fail the test are disqualified for one year — six months if they receive treatment — and are reported to the Florida abuse hot line. Payments to children can continue through another person, like a grandparent.

Since July, 7,030 passed, 32 failed and 1,597 did not provide results, according to the state. The state said it does not track what drugs caused failures, but elsewhere the vast majority of cases involved marijuana.