We are valuable for what we can do and not for what we can't do. Before jumping to the conclusion that something is impossible, one should make sure he understood perfectly the requirements, that he studied in depth all possible scenarios, that he consulted all available resources and tried to find all possible angles from which the problem could be attacked. I'm not saying that everything is possible or that one should hide if a problem is insolvable. All I'm saying is that it's really not ok for someone to start a priory by "we can't do that" without making sure it cannot be done under all circumstances.
BTW, requests that cannot be completed no matter what are very rare - usually managers and customers have a sense for what is absurd and what is not and don't ask for impossible things or, at least, are willing to discuss options. Most of the time it cannot be done because of miscommunication and lack of mutual understanding. Even under insane deadlines, something can usually be done, but may require changing the requirements and a close tracking.