I'll try to be as brief as possible. But it's worth the read.
The "DoJ agent" Carol was surprised to see the American flag on the tail of the plane. The only reason for this would be that she hasn't seen it in a while. This, along with the handshake in the end are the two key scenes that confirm the time travel theory.
To support this further, Carol looks out at the city from her hotel window. The intact buildings represent a view that's unfamiliar to her, an image that makes even a professional agent of her stature loose herself in thought for a second.
In this story, whoever controls the past wins the battle of the future. Therefore, the war is now waged in the past, where the stakes are higher but a lot more subtle. Joanne told Lorna in the forest that Maggie had said that humans are made for living in the woods. This suggests that Maggie's side is the one who's attacking from the outside (having retreated to the woods), so it suggests that they are considered the terrorists (terrorists are usually the ones fighting their way in, battling the establishment).
The "establishment" already has a firmer hold of the past. This is suggested by the fact that the "DoJ agent" Carol comes back in time more prepared, healthier and with memory intact (she's ready to receive her assignment, which she does, in a professional manner). On the other hand, Klaus has to look for Maggie in the streets, recognizing her only by tattoos, and then has to build her back up in the course of a number of weeks. This suggests that their side has lower technology, and that Maggie might even be their only shot (there's a lot riding on her).
Now, onto the war itself. For a reason that is unknown to me now, the stake is the little girl, Abigail. Another poster said that the Abigail/father scene with the drugs + laptop is proof of her brainwashing. To support this, she builds the dark cityscapes out of LEGO. We can assume that she is constantly shown horrible things on the laptop because she writes Terrorist on her colleague's backpack. In essence, this shows that she is being taught to hate the future "terrorists" that she possibly engenders (this might actually be the reason she is important). They are trying to cut the war at its source.
Maggie appears to have come back for one reason alone: to save Abigail from this situation, through Peter. When Peter is convinced at the end that Maggie was actually telling the truth (having seen the handshake), all that story comes down to is his choice: to take Abigail out the open door, or to return her to her class (and her life). Essentially, the choice is whether to lose the war right then, or fight for a chance. Or, if you want to look at it more philosophically, the choice is between having faith in Maggie or being conned by the establishment (notice the complete reversal from the initial perception of the movie).
That is why the picture is called The Sound of my Voice. It is the most important line in the movie, because it triggers his memory of his having a choice.
(Also, as a side note: my own theory is that Peter could be Maggie's father, along with Abigail being her mother. He has a complex flashback montage in the end during which one of the scenes shown is that of the blood that he gives, and that Maggie receives through the machines. A family member would probably make the perfect blood donor. But this theory is just speculation at this point, although he seems to have a complete revelation during that scene.)