As a historian with a specialization in military history, I can give you this very educated estimate. 2,230,115. Some things are very hard to estimate, namely casualties in some of the Plains Indian Wars and the Banana Wars, but that figure incorporates my best professional estimate. I'd say that's about as close a conservative figure as you can get. I'd be willing to accept up to 3 million as a liberal estimate.

EDIT: This figure only covers casualties I believe to be inflicted by US forces, not including allies.