I am going to tackle this from the leaderships standpoint since you put in that tag. If you are the leader of a team that is in a stressful period there are steps you can and should take.
First step is to send people home when they are tired. You are making the mess worse when you expect them to work to midnight, 2 am or what ever because tired people make huge mistakes that cost a lot of time to fix or worse don't get found because everyone is tired. As a leader, you have to model that while some extra time may be needed in the last week, it is not a way of life and when people start to get to the point where they can't think, it is OK to go home. You need to be monitoring the situation in real time (real leaders don't go home when their staff is working late!).
If some staff members are giving a hard time to others (especially about leaving before they do), you need to step in when you hear that and tell the person to knock it off. Projects do not benefit from this kind of interaction and as the leader it is up to you to stop it.
Next as a leader, you need to push back against unrealistic expectations and shield your team from them as much as possible. You need to have the courage to speak up and tell senior people that you sent the team home because they were exhausted and you need to tell people that you won;t work 80 hour weeks for months on end to meet a deadline that is artificial at best.
You need to monitor interactions between team members and step in to defuse the situation when tempers flare up. This often involves separating the people and talking to them individually and possibly sending one or more of them home to sleep. You need to let them take out their frustrations in talking to you (Which can be uncomfortable) rather than on their teammates. You also need to listen to their frustrations and do whatever is possible to reduce them. Even if you can't fix everything, knowing you will try to fix what can be fixed goes a long way towards reducing tensions. Sometimes, you may have to take someone aside and flat out tell them their behavior is unwarranted and must stop. Sometimes it might mean rearranging some tasks to separate team members who are not getting along under the deadline pressure.
You also need to make it clear why the stress is there and what the rewards will be to get through the stressful period. And you really need to think about rewards both in terms of money and other things that you can give them.
Most of all you need to make sure the team have some decompression time after the stressful project and doesn't jump into a new project the next day that is just as stressful from the start. This is especially true if some of the stress is coming from working too many hours. People are not machines, they need rest. You will finish the second project faster if you take a week where people can take time off or work at a less frantic pace before jumping into the fire again. You need to stand up for your team and make sure senior management understands this.
