Which is more important: To get the job done, or to take care of your people? What's the first responsibility of a leader?
On the one hand, the reason your team exists is to do something. If you're a non-profit, the point is to provide a service. If you're in the military, or a first responder, your missions tend to be immediate and real-world, sometimes even life-and-death. If you're in business, then you're a drag on the organization if you don't somehow help it make money. If you're in government, then society needs somehow to be better for citizens as a result of what your team does.
So there's really no point to you or your team if you don't get the job done.
On the other hand, if you don't look out for your people, no one else will. And if you burn them out or use them up, it won't be long before your team can't do much of anything at all. Besides, the real value in life resides in people, and it isn't right to do something for others at the expense of the people you lead.
So which is your first responsibility? Trick question: The first responsibility of a leader is balance. You have to do both.
A leader needs to know how much is reasonable to expect from his or her team, and when to encourage a little more effort and a little more sacrifice to get your job done. On the other hand, a leader needs to know when to ease up a little, recognizing that getting things done a day or two later will safeguard the team's ability to still be working a year from now.
The task and the team are equally important, so you need to take care of both equally. Hey, if it was easy, everyone would want to do it.