If you have high turnover and overall poor morale, then you need to coordinate with the leaders both above you and below you and consider overhauling something in your process, because whatever it is you're currently doing is pretty obviously not working. Unfortunately, your question is somewhat vague, so I can't give you better information on what exactly needs changed. It might be worth bringing in a consultant to help you identify specific things that need fixed, so here's some general stuff.
In short, if you're in crisis mode something went wrong. If you're constantly in crisis mode something is wrong with your system and needs changed yesterday.
In general, it sounds as if your projects routinely go beyond the scheduled time (or threaten to do so, and require overtime to keep it on track). This is evidence of failures in project management. Either the project manager genuinely doesn't know what the team is capable of producing in a given amount of time (ie - they think the team can complete a task in 2 days, when in reality, it takes a week), or they try to promise things faster, thinking the team will just work over to get it done. Either way, it spells disaster for the project, and burnout for the team.
Meet with the leaders below you (not just managers, but non-management employees that show leadership tendencies and have been working harder to help keep the project organized and on track) and find out how they feel. Very often, there is a disconnect between management and workers in situations like this. Management often thinks that something is wrong with the employees when something doesn't go right, while the employees find themselves under impossible deadlines and their jobs on the line for decisions made by higher-ups. Make the necessary changes to your fundamental way of doing things to prevent the crisis situations to begin with.
Some things to find the answers to (this is by no means all-inclusive):
- How are schedules determined? Are they based in reality? Does the project manager consider (or know) the capabilities of the team? Or are they based on what the project manager thinks the tasks should take, or (even worse) what the client thinks the tasks should take? Is the project manager using scoping techniques to determine timelines and time slack?
- Are members of the build team involved? The people that are actually building your products will know the best what timelines are realistic. Including a lead or senior member will help make sure that your project manager isn't overpromising.
- Does the schedule reflect reality? Is meeting time included in the schedule? A team may be able to finish a project in 8 hours if that's all they're working on, but if you're holding them up for 2 hours in a meeting, it's going to put them behind if that's not accounted for in the schedule. Additionally, some industries are prone to scope creep, which can turn a good project sour in a hurry. Make sure you're accounting for it by updating the schedule accordingly and enforcing the scope creep clause in your contract with your client (you do have one, right?).
- Is the project methodology you're using actually working for your projects? If you're a software company, using the Waterfall Method to develop, and your clients are notorious for wanting new features three quarters of the way through the project, then the Waterfall Method is not for you. Learn about and switch to an agile method to better adapt to your clients' and company's needs.
- Do you have reviews after project completion? I'm not just talking about reviews of the build team, but reviews of everything. Interview both employees and managers, and get their opinions on what went wrong and what went right. What worked? What utterly failed? What didn't fail, but could be better?
- Do you have a method of tracking and prioritizing tasks? If everything is of highest priority, then nothing has priority. You should have a system in place that communicates what needs to be done, the priority that each item has, what depends on that task (and what tasks that one depends on), and when the task is due.
Second - and this may seem counterintuitive - invest in your employees. They are the lifeblood of your company, without them, your company will fall, treat them accordingly.
- Instead of laying people off, hire more. This will improve overall morale because one, you're not putting people on the chopping block (which by default lowers morale, as their job security is called into question), and two, you're giving the project the needed man-hours without requiring large amounts of overtime from everyone, preventing burnout.
- At the end of these projects under the "old way of doing things," reward your employees with mandatory paid time off (ie - make them take a vacation so they can recharge).
- If you find that there are genuine issues with how the employees work (keep in mind that knowledge workers often work best with short breaks every hour or so; so make sure you're not mistaking the usual productivity cycles with real issues), get them training on time management.
- Cater their lunches, even if it's just a couple of times a week. This gives them one less thing to worry about, and shows that you care about them, boosting morale.
- If applicable, create a new company culture that allows for employees to pursue their own (work-related) interests. This allows employees to work on a different type of project than what they typically work on, boosting morale and helping stave off burnout.
Yes, these things will cost money, but you're losing far more money on turnover costs and failed projects. Additionally, these things have long-term ROI, because by investing in your employees, they will become more productive as they start to relax and actually find some enjoyment in their work.