This phrase is Canadian in origin, starting in the 1900s (as in 1900-1910) as 'close enough for government work'. There it meant it was up to the standards the government used for purchasing, which usually meant higher quality than average. The phrase spread to the United States where it was popularized during World War 2, either by Hollywood or American manufacturers (or perhaps both). In that case, the phrase represented not an inherent lack of quality but that the bureaucrats they were working for could not evaluate the work effectively and often gave specifications that were, by the standards of the industry, strange or incompetent.

The phrase became fully negative in the 1960s, perhaps a little earlier. But there it still only referred to the interaction of the government and the private sector. The phrase exploded in popularity with the sixty's anti-government sentiment and became a symbol of dissatisfaction with the government at that time.

From A History of the Canadian Parliament (the phrase's first appearance is in Parliamentary records on June 8th, 1906) and The Project of War: American Culture During World War 2.