Vincent Müller and Nick Bostrom have just released a paper surveying the results of a poll of experts about future progress in artificial intelligence. The authors have also put up a companion site where visitors can take the poll and see the raw data. I just checked the site and so far only one individual has submitted a response. This provides an opportunity for testing the views of LW members against those of experts. So if you are willing to complete the questionnaire, please do so before reading the paper. (I have abstained from providing a link to the pdf to create a trivial inconvenience for those who cannot resist temptaion. Once you take the poll, you can easily find the paper by conducting a Google search with the keywords: bostrom muller future progress artificial intelligence.)
The premise was a superhuman intelligence? I don't see how it could create a large enough botnet, or find enough exploits, in order to be everywhere moments later. Sounds like magic to me (mind you, a complete layman).
If I approximate "superintelligence" as NSA, then I don't see how the NSA could have a trojan everywhere moments after the POTUS asked them to take over the Internet. Now I could go further and imagine the POTUS asking the NSA to take it over within 10 years in order to account for the subjective speed with which a superintelligence might think. But I strongly doubt that such a speed could make up for the data the NSA already possess and which the superintelligence still needs to acquire. It also does not make up for the thousands of drones (humans in meatspace) that the NSA controls. And since the NSA can't take over the Internet within moments I believe it is very extreme to claim that a superintelligence can. Though it might be possible within days.
I hope you don't see this as an attack. I honestly don't see how that could be possible.
Given a backdoor or an appropriate zero-day exploit, I would estimate that it would take no longer than a few minutes to gain control over most of the computers connected to the 'net if you're not worried about detection. It's not hard. Random people routinely build large botnets without any superhuman abilities.