(CNN) -- Florida Gov. Rick Scott on Sunday defended recent legislation that requires adults applying for welfare assistance to undergo drug screenings, saying the law provides "personal accountability."

"It's not right for taxpayer money to be paying for somebody's drug addiction," Scott told CNN's T.J. Holmes on Sunday. "On top of that, this is going to increase personal responsibility, personal accountability. We shouldn't be subsidizing people's addiction."

But the ACLU of Florida, which has already filed suit against Scott over a measure requiring government employees to undergo random drug testing, disagrees, and may sue over the welfare law as well.

"What (Scott) is doing is giving ugly legitimacy to an unfortunate stereotype that has been in this country for a couple of decades -- that all welfare recipients are a bunch of drug abusers," said Howard Simon, executive director of the ACLU of Florida.

Scott told CNN he wants to ensure that welfare funds go to their primary target -- to disadvantaged children -- and provide people with an incentive not to use drugs. He signed the measure on June 1, calling it "the right thing for taxpayers."

Under the law, which takes effect on July 1, the Florida Department of Children and Family Services will be required to conduct the drug tests on adults applying to the federal Temporary Assistance for Needy Families program. The aid recipients would be responsible for the cost of the screening, which they would recoup in their assistance if they qualify.

Those who fail the required drug testing may designate another individual to receive the benefits on behalf of their children, and do not receive a refund for the test.

Shortly after the bill was signed, five Democrats from the state's congressional delegation issued a joint statement attacking the legislation, one calling it "downright unconstitutional."

"Governor Scott's new drug testing law is not only an affront to families in need and detrimental to our nation's ongoing economic recovery, it is downright unconstitutional," said Rep. Alcee Hastings. "If Governor Scott wants to drug test recipients of TANF benefits, where does he draw the line? Are families receiving Medicaid, state emergency relief, or educational grants and loans next?"

"I work for the ACLU, and it's our job to prevent trampling on the constitutional rights of people," Simon said. The Constitution mandates that searches cannot be conducted without probable cause, he said.

Controversy over the measure was heightened by Scott's past association with a company he co-founded that operates walk-in urgent care clinics in Florida and counts drug screening among the services it provides. In April, Scott, who had transferred his ownership interest in Solantic Corp. to a trust in his wife's name, said the company would not contract for state business, according to local media reports.

Asked about the company Sunday, Scott said he is in the process of selling his family's interest in the company and "it will be sold in a couple of weeks." There is no conflict of interest, he said.

On May 18, the Florida Ethics Commission ruled that two conflict-of-interest complaints against Scott were legally insufficient to warrant investigation, and adopted an opinion that no "prohibited conflict of interest" existed.

On the measure requiring public employees to undergo drug testing, Simon noted that public employees -- workers in city, county, state and federal government -- are protected by the Constitution and should not undergo "intrusive" drug testing without probable cause to believe a person is using drugs.