Imvvirgo,
Firstly, from the way you describe it you seem to be thrown in with little or no preparation and you know that it is not right, and it is not rational. So they are behaving irrationally. You say "For some reason they expect me to get done with it in next 3 months. My PM has arranged my first meeting so that I can ask 'intelligent questions'" - here is your first question: what reason do THEY have to think you can 'get it done in the next 3 months"? What is THEIR justification?
Besides, when they say "get it done" have they defined "it"? If not, that is your next question: What is 'it' exactly?
If they have defined 'it' what is the justification for the definition of 'it' and who came up with it (because that person is probably the person who thinks they are doing Business Analysis on this project - so why not get them to ask the "intellignet questions" etc).
And like Dave has said, why 3 months? Say you take 4 - what would happen?
If I was put in this situation I would raise the issue on the issue register that I have not been prepared enough and the risk that goes with it is the project will fail because of that issue. The PM owns and manages the risk and issue register so let him sort it out. Your recommondation would be to let you work out what needs to be done and then give him an estimate of how much effort is involved - not the other way round.
I know you are a young BA but are you experienced? If you are, just treat it as a new project which will take as long as it takes and start asking what the SMART objectives are, use those to drive out the functional requirements and resultant process and data requirements etc.
If on the other hand you are not experienced, you have just started with this company and have no real idea of who they are, what is happenning and what you should do I would suggest that you let them know that right now.
Bottom line: the best way not to look stupid is to explain to them (before the meeting if you can or at the meeting if you can't) these very real and material concerns. No rational person is going to think you are stupid for explaining that you have been given an impossible task!
Good luck!
Guy