The US welfare system does not work. Welfare is intended to give people the help they need in order to not need welfare anymore, but instead it has become a system where the government subsidizes corporations that don't pay enough to their employees. I believe it would be better to substitute it for the following:
16 hours of work a week in a civil service (building infrastructure, medical or education based work, administration of the new welfare program, farming, etc.), the government will provide for you and 2 dependents:
accommodation
medical care
2500 calories of food per day (a school lunch for children)
secondary education/trade school or childcare
This new program would use all funding from current welfare programs, so the only way to receive benefits would be to participate in the program. The only exception to this is severe mental or physical disability that would prevent a person from doing any type of work.