Other government programs disqualify those who have been convicted of drug offenses. In particular, students cannot receive financial aid for college if they have been convicted of a drug offense. It's reasonable then that those who receive federally funded assistance also be required to avoid the use of illegal drugs and substances.
Those who are on welfare should totally be required to get drug tested. I don't believe that positive tests should mean no benefits though. In fact, positive results should be used as a reason to get them help to get clean and on their feet, which most of them probably want. Welfare is part of that
Yes, there should be a drug-testing requirement for individuals who accept welfare because the government has a responsibility to ensure that public money is spent appropriately. Individuals who use illegal substances usually resort to illegal means to obtain those materials. It would be easy for individuals on welfare to trade their public assistance for drugs, so the government should monitor welfare recipients for illegal substances.
There are no valid arguments to drug test welfare recipients. When local governments have practiced this, it cost the government more money to drug test the recipients than it saved by ending the benefits of those that tested positive. It also unfairly targets welfare recipients, when many other people and groups benefit from receiving government funds.