One of the hardest situations for a project manager to manage is the one were she is the new guy/gal in an organization. The 'new guy' almost always gets the projects that other people don't want or that are in trouble. Being the new person you have less leverage or ability to either say, "no I won't do it", or "this is wrong, we need to re-calibrate". The internal pressure is on to prove ones self and/or to confirm people's decision that they were right in appointing you in the first place. It is this internal/personal wish, desire, or motivation that drives us to accept tasks that our professional competence tells us are if not impossible, then extremely risky, not only for ourselves but for our employers.
How do you handle this? As soon as you realize that you are up the creek without a paddle then you have start documenting the real situation. Make sure that your status reports indicate the true state of affairs and let the stakeholders make the decisions. Always record your findings and make sure any changes in your findings by other people are documented.
I was on a project that was doomed by the time I was assigned to it. Strategic decisions had been made which precluded almost any chance of success. However, when I decided that we needed to report that the project was at risk I was overruled. It would 'upset’ people I was told, so we had to leave it as 'on schedule'. Unfortunately for the person making that decision he actually wrote that opinion in an e-mail. So when he tried to blame the miscommunication on others his "goose was cooked". So trust but not too much! When in doubt document, is a pretty good working motto.