It depends entirely on the structure of the welfare program. For example, the veterans affairs administration provides services, mostly health services, directly to veterans. In that case, you'd expect 100% to be overhead, because VA doctors and hospitals are paid out of overhead.
Most federal welfare programs, however, involve cutting a check. Look at the Social Security Administration. It has a budget of about $12.7 billion, and administers $700-800 billion in benefits to 50-60 million people: http://www.ssa.gov/pressoffice/basicfact.htm
That amounts to an overhead of 1.6%, or ~$250 per person served.
Or, look at it another way. Total federal payroll is about $180 billion, for 2.15 million federal employees (a number that has fluctuated between 1.8 and 2.2 million for the last half century despite nearly a doubling of the population). That's about 4.7% of the budget, or 1.2% of GDP.
Most of the federal government is not overhead. 95% of it is just taking in tax revenue from certain people and cutting checks to other people.