Half the welfare money does not go to staff or administration. The biggest cost in the welfare budget in every state is Medicaid, far and away. That is payments to hospitals, nursing homes, doctors, etc. as reimbursement for services. We can argue as to whether those payments are too high, whether people who shouldn't be covered are covered (like illegals), etc. But it's a myth that administration is where most of the money goes.
If there's waste in welfare (aside from the illegals issue), it is the way that people with decent incomes (NOT poor) find ways to qualify for Medicaid and other programs. In particular, the games played with estates so that the taxpayers end up subsidizing someone's inheritance. Or the assumption that every person receiving a government service must be dirt-poor and can't possibly contribute part or all of the cost of the service.
There are lots of things to cut in welfare programming. But the assumption that there's a $1 billion program out there called "waste, fraud, and abuse" that can simply be cut and everything will be hunky-dory is wildly optimistic. And how do you think fraud and so forth is prevented? That requires just a bit of staff, doesn't it?
I don't work for any social welfare agency, but I do know that most of those people are overloaded and stressed out as it is. Lay off more of them and you'll create workloads that will end up with them leaving in droves, and pretty soon you'll have inexperienced people making tons of mistakes and the waste, fraud, and abuse will increase.
They just sign up. They advertise food stamps to families who make more than 2 grand a month these days! I've heard these ads with my own ears.