Well the laws of physics means it would take some finite time from the initiation of the singularity to the end of all life even if the singularity was extremely hostile to humans.
Well, a huge percentage of people who are actually working on the AI field (unlike Hawking, Gates and others) disagree with you: http://www.nickbostrom.com/papers/survey.pdf (warning: PDF (obviously))
And the majority was never wrong, of course.
What makes you say that?
How long before “it” decided we were outdated and obsolete?