here is the drug test kit Dr. Drew uses on Celebrities - they go for under $6 each kit (a box of 2) and very cheap in huge numbers - imagine what the Feds or States could pay for them.
It takes 5 minutes to show results on up to 10 different substances. Let them fail once, but if they fail a retest one Welfare Check Later, boot them from the system, give their kids to people who want young children but can't get an American baby and settle for Haitians, etc..
I even would go for a mandatory rehab program (let's make jobs in this country) even if it is rehab and drug testers for welfare recipients. If they fail at any time for drugs during rehab, then they definitely go and kids are taken to a safer environment.
Here is the $6 for 2 test kit - add a system for implementation to test and clean house.