The states are among 36 that considered proposals this year linking benefits such as welfare, unemployment, food stamps, public housing and job training to results of drug tests.
Supporters say the policies ensure tax dollars aren't paying for drug abuse.
Opponents say the tests are based on stereotypes about the poor and that those receiving public assistance are no more likely than others to use drugs.
Laws linking benefits to drug tests have passed in states including Arizona, Indiana, Missouri and Florida, the Times said.
Florida requires those receiving cash assistance through welfare to pay for their own tests, and enrollment has fallen to its lowest level since the start of the recession.
"To me it's real simple: Money is going to go to the benefit of children, not to a parent using drugs," said Florida Gov. Rick Scott, a Republican who campaigned on the proposal.
The American Civil Liberties Union filed a lawsuit last month challenging the law, saying the requirement violates the constitutional protection against unreasonable search and seizure.
Kimberley Davis, director of social services at Operation Breakthrough, which provides daycare to low-income women in Kansas City, Mo., said the state's required drug testing reinforces stereotypes.
"All this does is perpetuate the stereotype that low-income people are lazy, shiftless drug addicts and if all they did was pick themselves up from the bootstraps, then the country wouldn't be in the mess it's in," Davis said.
Most of the proposed drug-testing requirements have not won necessary support because of concerns about their legality dating to a federal court ruling a decade ago.
In that case, a court struck down a Michigan law that required drug testing for all welfare recipients, saying it violated the constitutional protection against unreasonable search and seizure.