First Dawn Book One in the Lost Millennium Trilogy - Mike Shepherd

How do you win a war lost 6,000 years before you were born? Those are the orders waiting Launa O'Brian, fresh out of West Point. They want her to help peaceful farmers win a war they're about to lose and beat back the Horse Raiders that destroyed them.
The Army has a time machine. They even tested it once. It didn't work, but trust them, they fixed it. With the whole army to chose from, they've assigned her Captain Jack Walking Bear as a partner. As a captain, he outranks her. As a guy, he's got a lot of different ideas about how to run this show. But the President put Launa in charge, because his old anthropology professor says women spoke first back then and guys paid attention.
So how come the first thing they see is a war band of horsemen who want to hit them over the head and steal everything they brought? Did the time machine blow it? Were the anthropologists overly optimistic?