Here's an interesting interactive graph from the New York Times that shows the share of people's income that comes from government benefits programs like Medicare/Medicaid, Social Security, Veterans Benefits, Unemployment Insurance and Income Support. The graph breaks this down by county, so you can get pretty specific in terms of what you want to know. In the U.S. all government benefits account for 17.6% of American's income. This number has increased from 8% in 1969.
I'd like to see a more specific breakdown of this number. I'd hypothesize that this shift is largely due to the economic policy changes that began in the 1970s but really took shaped in the 1980s and 1990s, namely neoliberalism. It would make sense that people would rely more on the government as a source of income as neoliberalism produced a decline in unions (which provided working class people a means to achieve middle class status), more temp work, a shift from a manufacturing based economy (that tended to pay better) to a service based one, a reduction in employee benefits, and movement of semi-skilled jobs out of the U.S. in search of cheaper labor and fewer environmental regulations (often moving to the global south).
Based on the graph, Social Security accounts for most of the cumulative benefits (5.6%), while Medicare is second (4.1%), then Medicaid (3.1%). Veteran's Benefits account for a little over (1%) of the total. I don't recall exactly what government agency funds Veteran's Benefits, but it's not the Department of Defense. I think it's the Department of the Interior.
Check it out.