Antagonist
Character Role Analysis
The War
There are plenty of antagonists in Sunrise Over Fallujah: pretty much anyone who Birdy and his squad are working against in any of their missions, from the people who shoot at them to the people who won't give them the information they want.
But they're just a distraction. The real antagonist is the war itself.
Birdy and his squad are continually trying not to get killed and not to get depressed from all the violence. The war affects them even when they aren't fighting, and they each have to use their way (Birdy with his letters, Jonesy with his blues, Marla with her sass) to stay positive and remain themselves in the face of it.