A disaster recovery project is one with a tight deadline and fixed deliverables. If it looks like there is no way for the project to succeed - then congratulations, you have a disaster on your hands.
Beyond that basic description disaster projects can vary a great deal. You might be dealing with a raging fire, trying to get a building finished for launch day, or taking over a botched IT deployment. No matter what the details are there is a common approach that can be applied to make the most of the situation.
Step One: Smile!
Relax, this is going to be fun! Pragmatic project managers who get hard things done are respected and this disaster will give you a chance to prove that you are that kind of leader.
If this disaster is your fault you might have a little less fun, but if everything went perfectly all the time no one would need project managers in the first place. Unless you own a time machine the only things you can change are in the future, so that's what to think about now.
Step Two: Think about immediate action items
You need to create some breathing room to get on with planning. There are probably some obvious tasks that need to be completed, asking the team to get going on these will stop them showing up on your critical path later on.
Don't worry too much about picking the wrong tasks to start first, the goal is to balance the risk of wasting time through inaction with the risk of doing things that don't need to be done.
It's worthwhile explaining to the team why you are asking them to get started on the immediate action tasks. There will probably be a change of plan later and if they expect it then it won't cause them to doubt your ability.
Step Three: Establish which constraints are actually hard
Some of the 'must do' deliverables on your list can probably be sacrificed if it means the difference between partial success and total failure. Take a close look at which requirements are critical, such as nuclear safety, and which are nice to haves, such as being exactly on budget.
This isn't the right point to talk to stakeholders as you will need some options to present them with. Just keep the possible trade-offs in the back of your mind for the next stage and remember that you are doing damage mitigation not green field planning.
Step Four: Create a new plan
Now you know which constraints are non-negotiable it's time to start sketching out a what-if plan to see how you can get those things done.
Start by listing out the constraints, then the things you need to do to meet those constraints. Keep a running total of the time, money and other resources required for the things you have listed so far.
If you run out of resources before you finish adding everything to the list then take another look and pick a constraint to drop. It's better to deliver something than nothing, and if they are all equally important then you should drop one off the list at random.
If you get to the end of the list of hard constraints and still have time on your project plan, then you can add some of the lower priority items you identified in step three.
Now you should have a list of the things that can be done, and the tasks required to complete them, plus a rough estimate for each task. That's enough data to draw up a PERT chart and work out the critical path. There are tools to help you automate this process, or you can do it by hand.
As you have identified the critical path you now know what the team really need to work on, letting you shift people over to the most critical tasks.
Step Five: Set expectations
Because you have an idea of which constraints need to change to make a workable plan, it's time to start engaging with your stakeholders about what you have discovered.
It doesn't matter how bad the situation is, the sooner you update them the better. Recovery takes time and if you don't explain the situation now then your successor will explain it later.
As you present your plan don't forget to include (and highlight) a buffer of contingency time or money, otherwise there will be another disaster along soon.
Remember to incorporate whatever feedback your stakeholders have as they may want to work to different constraints, but you will do them no favours if you cave in to trying to do everything. Because you spent time planning out the options you know which constraints are realistically achievable and have an understanding of why that is. This means that you can explain coherently why things can't be done.
Step Six: What next?
If you can get any agreements in writing, but the main thing now is to get on with the job and haul yourself out of the disaster. Good luck!