Don't sweat anything--not the big stuff, not the small stuff!
Of course, not sweating anything doesn't mean one shouldn't care because one should--one must--care deeply about the institution. It does mean--for one's health and the health of the college--one must keep one's equilibrium, since the health of the college will deteriorate as quickly as one's own health does. No, one is not indispensable, but, because one is president, one needs to do everything one can to advance the college--and one can't advance it if one is mentally or physically run down.
While pushing oneself harder than those with whom one works, don't forget to stay balanced. Often in my first presidency, I'd find myself sitting with a vice president after others had gone home, when one of our wives would call to summon us to dinner. It took a while, but I finally worked out a schedule that allowed me to balance properly my professional and familial responsibilities.
Later, when I became a single father, juggling became a bit more challenging. I was able (I believe) to do my jobs reasonably well--both of them. I never missed my older son's plays (or even a performance of a play) or my younger son's soccer games. Well, I did miss one soccer game (which happened to be the state finals). As a result of heavy rains, the game was switched to Commencement Sunday. Much as I wanted to see my son play, it was clear where I had to be that day.
One will constantly be at everyone's beck and call; one will be dragged and pushed simultaneously in several directions. At first, the temptation will be to do whatever one is asked to do. Then the realization will set in that one has to make choices.
Make those choices--and make them in a way that allows one to maintain one's equilibrium.