Stress Increases Efficiency?

I've observed that there seems to be some correlation between Stress and Efficiency. It seems like the more stress I have (maybe due to a shorter deadline), the better is the quality of my work. The more time I get, the lower the quality of my work. 

I posted this as a Whatsapp status and my friend replied with an interesting take on this. In Animals, stress response is a crucial aspect of defense mechanism. For example if a Goat is being approached by a wolf, stress harmones release and only then it'll work towards it's defense. 

Building up on this I reached a conclusion that perhaps my reports/ quality of work is higher when I'm under stress is because of the defence mechanism. In trying to protect myself from negative outcomes and cover for the delay, I subconsciously seem to be giving it my best.