I’m sorry for your situation, that’s inexcusable on your manager and his manager’s part. Not only should they articulate why the deadline was tightened, but why it was important for the company, them, and you. They should understand the crunch, empathize with their staff, and work with them to come up with a plan to achieve the goal together. If you have future leadership aspirations, take this as a lesson on how not to do things…
When I find myself in these situations I push back up, not to resist, but to discover more details, armed with that you can expedite criteria or find more creative solutions to accomplishing the project. Be inquisitive from the standpoint you are trying to learn more to put a plan together to achieve the goal. If the net result of the answers you receive leads you to believe it truly cannot be done, then communicate that message with options and solutions as Cyberdemon said.
If you get stone-walled in your attempts to do this, and more specifically if you are told to “just make it happen”, then bail once you find another opportunity, even if it is in the middle of the project. Bridges have 2 ends, sounds like the fire was lit on their end, it happens, you can choose not to refer colleagues to work for them, that is a two way street. If you’re early in your career don’t sweat it, but do exit professionally, and lean on your portfolio as it can prove to be your best reference.