As this makes clear, the big sustained drop in poverty has been among senior citizens. And I think that should be no surprise as Medicare is the largest and most sustained Great Society program. The scope of Social Security was also expanded a lot during the 1950s and I believe it was made more generous during the 1960s. It also seems that you can’t claim any substantial Great Society success in terms of reducing the poverty rate among working-age people, aged 18-65. For kids, it looks to me like you had some meaningful progress that’s since been partially reversed by the changing demographics (for ideas on how to create new reductions in child poverty, check out CAP’s Half in Ten program).
So to be charitable to critics of the “war on poverty,” I think you can say that even though the Kennedy/Johnson years were a big success in terms of reducing poverty, the specific initiatives undertaken by the Office of Economic Opportunity were not at the forefront of this success.