Of course you are not going to solve all your crises in three days, but the allegory is useful in describing how you have to stage your work. Remember, everyone around you, including perhaps your boss, may be in a high state of panic when you arrive on the scene. Take the point of view of the Texas Ranger who got off the train alone, to the consternation of the townspeople he had been sent to help. "We wired that there was an insurrectionwhere are the others?" asked the elder statesman of the group. "One insurrection, one Texas Ranger," was the reply. You must remain calm while everyone else is up in arms.
The "odor" on the project can take many forms. The rumor mill will make sure of that. In the early days, one of your jobs is to understand the root causes of the odor. Is the software simply late? Are large parts not working? Is the user interface clumsy? Is the build process broken? Has sufficient testing been done? What's the state of the documentation? Is the team in open revolt? Have the marketing people gone ballistic? All these and other smells will be in the air.
Getting rid of the odor means doing the "public relations" part of the job to stem the tide of negative opinion now surrounding the project. This means you need to be able to calmly respond that certain problems reputed to exist really don't or are not critical. And, for the other legitimate causes of odor, you need to freshen the atmosphere by publicly explaining what the "get-well" plan is.
So your first and most important task is assessment. You must get first-hand data on what's going on, and you need to make quick and accurate judgments about the people you talk to. Some of them are going to be instrumental in helping you out of the mess, but don't forget that some of them are the reason for the mess in the first place. So think in terms of who stays and who gets moved down the road. You must have team players who will get on board with the new plan; those who seem especially resistant to change are going to be too high overhead to be useful.
As you assess, you need to be moving as rapidly as possible into figuring out and beginning implementation of the new plan. This must be done before any attempts at damage control are undertaken. Until you can explain how you are going to do things differently, you really have nothing to say. Resist at all costs going public with opinions until you are confident of your assessment and have at least the outline of a plan ready to talk about. There will be a lot of pressure, because people want reassurances that "things will get better." Well, you can't do that until your get-well plan is underway.
Once the new plan is underway, then you can turn some of your attention to the damage control part of the job. It is important, don't get me wrong. But you can only do it effectively once you have done the other two activities to the best of your ability.