That's first. Obeying lawful orders is second.
It's debatable how this oath applies in Manning's case, but I think it's rather telling what order the things you are swearing to uphold come in.
When I was in the military my interpretation was that anything I was ordered to do that was contrary to the Constitution was an unlawful order. If I were taking the oath seriously, that would have required active dissent, not just ignoring the order.
http://usmilitary.about.com/od/joiningthemilitary/a/oathofen...