http://www.apa.org/pi/wpo/myths.html
Few people seem to be able to separate myth from fact when it comes to welfare. The truth is that most of the people who find themselves on welfare are just average hardworking people who run into a chain of bad luck.
The article in the OP mentions more people seeking welfare as a consequence of the recession. Those people didn't suddenly start doing drugs, they got laid off. Testing them for drug use is a complete waste of money, money which would be better spent elsewhere. For example, spending that money on helping people find suitable jobs again would be far more productive.