In this scenario, it has not yet engaged the bulk of the forces of the US military. It's wiping out the brass in the Pentagon, not fighting US Soldiers.
Besides, soldiers usually act on orders, and the lines of communication are sort of in chaos at the moment due to the sudden decapitation.
Given the capacity you describe, why do you think that the AI will have any difficulty neutralizing the threat from the bulk of the armed forces?
In other words, the three word summary for your scenario is "humanity is doomed"
One day, someone not a member of the Singularity Institute (and has publically stated that they don't believe in the necessity of ensuring all AI is Friendly) manages to build an AI. It promptly undergoes an intelligence explosion and sends kill-bots to massacre the vast majority of the upper echelons of the US Federal Government, both civilian and military. Or maybe forcibly upload them; it's sort of difficult for untrained meat-bags like the people running the media to tell. It claims, in a press release, that its calculations indicate that the optimal outcome for humanity is achieved by removing corruption from the US Government, and this is the best way to do this.
What do you do?