If you're wondering why everyone is downvoting this post, this is a good place to start. While there are some existential threats that humanity could fight against after they're out of the bag (plagues, for instance), post-intelligence-explosion AI is very probably not one of them.
(Of course, an AI might be able to pose a threat even without being capable of recursive self-improvement, and in that case the threat might conceivably be significant but not beyond human capacities. But your particular scenario is more a cheesy sci-fi pitch than a realistic hypothetical.)
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?