-era program in which surplus cheese
produced by ordinary American dairies was bought by the government and distributed to the elderly, welfare recipients, reservations, school cafeterias, and other food programs.
It was American loaf cheese, the kind Kraft makes into individually wrapped singles, and was supposed to melt very nicely. It is often compared to Velveeta, though this was real cheese, not a processed cheese food. It was pale yellow, and came in a large white box with CHEESE written in large black letters on it. Reports on its quality vary, but most agree that it made great macaroni and cheese. Those who complain about its taste seem to do so with a bitter memory of poverty, or an abhorance of Reagan's politics.
By synecdoche, "government cheese" has come to mean welfare in general. Almost as often, it is used to refer to corporate welfare, in that it was a government subsidy to dairy producers.
Buying surplus cheese does support prices and therefore stabilizes the industry. However, this comes at a cost for farmers: since there are always warehouses full of (at that point) free government cheese, prices on cheese are supressed as well--someone full of government cheese isn't going to buy IWPs (Individually Wrapped Processed cheese slices), as Kraft calls them internally. Kraft, the Goliath of the cheese industry, was pretty unhappy about the competition, too.
Anyway, by the mid-1980's, the Reagan administration, true to their supply-side philosophy, decided that the solution to excess dairy products was to buy and liquidate dairy farms, rather than buy and give away dairy products.
For what it's worth, concerning the remaining definition of government cheese, I happened to talk recently to a woman who volunteered for a government sponsored drug research program. Apparently your mileage may vary because here is her direct quote: "Let me tell you, your government grows some primo weed!"