I don't think we'd be screwed, but we will be forced to adapt.
What will probably happen is we'd take control of our own evolution and improve ourselves. Bigger more efficient brains, Longer lifespans, Stonger and faster, Better reaction times, More resistent to infections etc.
Probably possible if we can make sentient robots. Furthermore thats not taking into account any cibernetic advances aswell.
We'll change, a future with sentient robots isn't neccesarily one that means our inevitable irrelivance. Humans are very adaptable and with furhter advances into technology we'll probably be able to readily influence this adaptability and use it to our advantage.
EDIT furthermore, if a robot has a big enough synthetic brain to be considered sentient then surely it would probably be prone to daydreaming, boredom etc. They will be able to do many things more efficiently then us (in our current state) but that certainly doesn't mean that there isn't a cost involve with becoming self-aware. A machine that is sentient probably wouldn't want to work 24 hours a day like a mindless machine does. They will probably demand holiday pay etc aswell.
