I can agree to a certain extent. Seeing your tax dollars go to waste is frustrating, but this would really just add another problem to the system. For one, urinalysis is pretty expensive. You would be wasting money by testing people who don't do drugs, and people who do drugs will just find a way around it.
I think the problem is the idea that you can take money from a hard working individual and give it to somebody who is not, and then expect for that person to conduct himself in a more responsible manner just because of the fact that he has gained wealth they did not earn. I understand that some people really do get hit with problems that are completely out of their control, and that's why we have these safety nets.
My mother kept my siblings and me fed with welfare money and food stamps for a few years until she could take care of us without the need for additional help. Of course, our economic position was a reflection of her character at that time, so she did not spend all of the redistributed wealth in a responsible manner. In the end, however, these safety nets worked how they were supposed to. But waste and abuse is a by product redistributing wealth, and adding another layer of expenses with the intent to clean up some of that waste and abuse will probably just lead to more of the same. You shouldn't trick yourself into thinking all, or even most of the people receiving redistributed wealth are responsible people, and you really shouldn't think that the irresponsible ones out of the bunch can be socially engineered into becoming responsible.