Q:

How to deal with the stress of being in the middle of the chain of command

I am a manager for a team of people.
My boss sets my team very ambitious goals. To reach these goals my team needs to work a lot. He ignores and reacts badly to my arguments that it's too much.
On the other hand, people "under me" hate me because of setting the goals so ambitiously and making them work hard. If only they knew how much stress I had trying to "defend them" in front of my boss and how much criticism I got for it.
I've tried stressing to them it's what I get from my boss, but I can't tell them I'm against it of course.
What is the best way to deal with this kind of problem?

A:

Your boss is putting pressure on you to deliver unrealistic work. Your mistake is relaying that same pressure onto the team and assuming that will cause them to deliver said work.
It won't.
It'll make them less productive (with the attitude of "Nothing I do will be any good for this guy, so why put in the effort?") and pissed off at you to boot.
Your job as manager is to resource your team so they can work most effectively, and shield them from this undue pressure from above as much as possible. If that means taking a rap from the boss, and trying to convince him constantly that his workloads are unrealistic, then that's what it means. (Whether you want to stay in that role with that boss over you is another matter entirely.) 

A:

Yep, that definitely sucks.  This may sound crazy, but my advice would be to avoid thinking of yourself as being in the middle - but as someone who translates between two groups (employees, boss) who have two different sets of expertise.  It may still be unavoidably stressful, but at least it's something different to think about...
For the boss...
Consider yourself the subject matter expert on how your team's work gets done... you know how much someone can do it a day.  You know what the risks are to going faster than that (not just that people will quit... shoddy quality, failure from lack of due diligence, etc).  
Engage with the boss on that point - "our current metrics are X per person per day, you want X+50.  Last year we did thing-a to move from X-10 to X, but I think we've tapped thing-a... I can't see what step we'd change or shorten... can you...?  And X+50 is twice as fast as we go right now..."
He may have an idea in the back of his head... Or he may never have heard your numbers -- but at least you are talking about facts and not judgements.  "We'll never be able to go that fast" is saying the same thing, but it's not substantiating your assertion - which lets your boss see that as an opinion.  Giving real numbers makes it seem more like fact, and less like opinion.
Second - ask him why.  Let's assume he's not evil.  What is the business reason for needing to work so much harder?  Will not getting done in a certain time mean the company is out of business?  Is there no one else/no other budget that could help?  What's that bigger picture?  Similarly, if your team is being asked unfairly to work harder than every other team in the company - why?  That may give you play that you didn't know you had to solving the problem differently...
Relate that to the employees
At the very least you can say "here's why I'm asking for this..." - employees generally do want to do the right thing for the company.  If this is the difference between being in business next year, or being bankrupt, everyone may want to know that the situation is that dire.
Similarly - engage them in trying to find a better way - instead of just "I need X+50 a day" - try "we need to increase the joint productivity to (X+50)Xnumber of employees -- I don't want any of us to work every weekend - what risks can we take to work faster?"  Even if the answer is that you are screwed, at least you all reasoned it out together, and it puts you a little more on their side.

I'm not saying you're going to find a magic bullet... you might find something, but it's no guarantee.  I'm just saying that as a manager, I get a whole lot better feedback from my folks when I listen to their ideas and can relate our technical work to a business objective.

