Every time I have given a "I do not know, I have never done anything like this before, it will require research, it may take a few days or it may take a few wee

Every time I have given a "I do not know, I have never done anything like this before, it will require research, it may take a few days or it may take a few weeks" the response from the manager asking has always been: "So can you do it by X". Where X seems to be totally arbitrary from a dev perspective. I have never had a manager say "Ok, get to it and keep me informed".