As always, though, it isn't the stress that kills you but how you react to it. The only thing I can do is eliminate as many variables as I can and prepare for everything I can't. I can sit there and let my stress control me, but in the end I have to do what is best for the people under me and make everything work. The funny thing about it is that the best way to handle your stress in a situation where everything sits on you is to basically do your job and give everybody under you jobs to focus on as well.
My position is a little different, of course. Coaching an improv troupe full of high school kids in the end is about entertainment. So I have to sort of rule over them to make sure they "obey me and have fun". I do the best I can by simply making sure everybody is enjoying themselves, but at the same time they need to make sure they're falling in line.
In something like this it's easy to be a friend and have fun with everybody else, but there is also a goal we are striving towards. If I don't lead them to it things will never get done, so the important thing is to make sure everybody is doing what they are supposed to. An interesting point to make is that by doing that, I am doing what I am supposed to do.
Authority figures have a hard job in that, while some of them operate with little to no command over them, they are actually more accountable for how things get done than anyone they oversee. Teachers don't sit at their desk texting people while kids in their class are doing presentations (or at least I certainly hope not), because that simply isn't an action one can take.
Subordinates do have a choice. They can do their job, or they can choose not to do it at their own risk. But a good authority figure doesn't have that choice. They have an expectation to make sure everything is done right, even when it's stressful or physically hard, they have to do it.
I suppose this all falls down under maturity levels and whatnot, and of course there are exceptions to every rule. There is always room for improvement in everything that exists. But as soon as one sits down and says "I don't like it but it needs to get done", they have grown as a person. And growth is the single most important thing to achieve more with your life. It takes time, but it does happen.