While we can argue management's culpability for creating untenable schedules by trying to do too much with too few crewmembers, remember that it is ALWAYS the crewmember's responsibility that they be fit for duty; FAR 61.53, Part 67, the back of your medical certificate, and very likely somewhere in your FOM says as much.

If you are fatigued or sick, don't fly - you have a responsibility to yourself, your fellow crewmembers, and your passengers...to say nothing of the FARs. Believe me, I know its easier said than done...