What circumstances could justify getting an extension on graduate admission offer deadline?
Most of your colleagues are going through stressful scenarios right now as well, finishing up exams, projects, term papers, and the other parts of their undergraduate careers as well. So it’s unlikely that you’d get an extension just because of deadlines. 

If you had extreme extenuating circumstances—personal illness, family issues, or other events—you could make a request that is more likely to be accepted. But in general, there’s not much you can do.