That's the price of the lean organization. Some must die for the bottom line.
And time and time again, I've been told the answer was a resounding "yes" by employers, investors, managers, etc., yet when I answered "no" (usually because my inadequate technical skills), the world continued to spin, my business continue to exist, and my technical abilities continued to slowly get better.
While the wily freelancer / engineer should always boost his safety margin by telling his boss 6 months minimum when he's done it before in 2 months, I've found through experience the best thing to do regarding minimizing my own internal stress is to admit to myself that I don't need to be the best, the "A" student, the hotest new company, 30 under 30, or what have you. Instead, it's far more critical for me to enjoy my work and make enough money to survive comfortably in 2015. If the vicissitudes of life (in the form of my boss, investors, clients, etc.) decides to give me success, then great, but if not, I'm content being humbly myself.
To someone who hasn't gone through a career related burnout, failed a business, or whatnot, the above spiel probably sounds like the fatalistic whining of a weakling. The fact is, there is no sense pretending (especially to yourself) that you're somehow strong or a badass. It's much better than to cast out pride, get verbally peed on by your disappointed bosses, and do things at your own pace than it is to push yourself to the point you come to hate the thing you've invested so much time into.
I agree most business owners wouldn't believe anything close to "some must die" - however, I do believe that inaction is almost as bad, and I do think mental health / wellness doesn't get anything like enough thought or attention. The harder you work your staff, and the more pressure you heap on them, the more you have to focus on them as individuals and support them better.