The savings would be minimal since most of the people on gov't assistance aren't committing fraud. Plus searching for fraud and policing the system would require hiring more state employees to actually find the people who are committing the fraud, prove they're committing fraud, and then preventing them from doing it again. All that is going to require money to do and let's not forget these new Republican governors are firing state employees to balance their budgets. You can't fire state employees because we need to balance the budget and then turn around and say we need somebody to catch people who are committing welfare fraud. Because those somebodies would be you guessed it, state employees.
Then it's going to cost money to administer and process the drug testing. That's also going to cost money. And since we're testing EVERYBODY on welfare that would include people who aren't using drugs so basically your wasting money there. Then of course we all know it's impossible to cheat a piss test . These drug test would be most likely piss tests since they are the cheapest tests that produce a fast result. The only way somebody can't cheat a piss test is if the person administrating the test actually watches the person take the test. And that's sort of perverted and IMO worse than an intrusive airport screening. We saw the outrage over the old woman who was forced to take off her diaper at the airport. Just imagine the outrage over an old woman like her being watched while see takes a piss test just so she can get some gov't assistance. So it's unlikely they'll watch people actually piss into the cup which enables those who want to cheat the drug test to do so. So you'll still have people who use drugs on welfare.
But most importantly as I already said, it infringes on a person's civil rights. The second a law like that was passed it would go directly to the courts and end up being ruled unconstitutional.