I just had a talk with a friend and he claimed that Avatar (2009) was the first film that got an American audience cheering for American soldiers being killed. I tried to offer several counter-examples, but he dismissed them:
Apocalypse Now (1979) - The protagonist is also an American soldier working for the American government, so the message is that only some parts of the American military should be destroyed and not the whole thing.
The Last Samurai (2003) - The antagonists are Americanized Japanese, and not actual Americans.
Castle in the Sky (1986) - The film is Japanese, not American.
Full Metal Jacket (1987) - The film has you cheering on the American soldiers and then shows how horrible you were for doing so be revealing the enemy sniper is a young women begging for death. The film does not actually get you to cheer against the Americans.
I know that Hollywood has produced films critical of the American military since at least the 70's, so I am willing to bet that there is a film out there that would work. However, I am not much of a film buff, so I can't think of it.