I agree! You will go crazy if you don't have a more exact count of guests...it's really hard to plan things without this info...
We sent out a formal invitation with a very specific RSVP date. We requested that our guests book everything by a certain date so that we could go ahead with our planning. I don't think it's too much to ask for a deadline...you might get a few people who miss the deadline, but at least you will have a much more accurate count...
For us, we requested that our guests confirm everything about 3-4 months in advance...
Good luck!!