What Should I Work On Today?
At this point, you’ve told the boss that you will not hit the date. You have reframed the problem from a personnel problem (you are late) to a project management problem (someone needs to adjust the schedule to reflect reality). The next question is this: "What should I work on next, boss?"
This question preserves the manager’s sense of control and gives him choices. If you have to be explicit, ask, "Should I work on features or fix bugs? What features? What bugs?"
The doomed-ness is now at the feet of the manager. Do your best, be professional, and stay committed to the project, but you can now officially stop feeling bad that you cannot do the impossible. (But if by chance you’re doomed a lot and no one else in the organization is, seriously consider whether you are cut out for the role you are currently assigned.)
Nine times out of ten, the original due date will come and go, the company will survive, and your job will be safe. If the organization is going through some internal meltdown and your job really is in jeopardy, I hope that I have helped you recognize the unreasonable management, and you have been working on an escape plan.