The answer depends on several factors, including the time of year you're doing this, the day of the week you want to stay and your flexibility with resort and room size. DH and I had the exact same concern before we purchased in December. We travel a lot for work and tend to make last-minute trips with little planning. However, we also do several planned trips a year. What we have found is yes, you can make short-notice reservations WITH exception. If you are going Easter week - forget about it. If you HAVE to stay at BWV - forget about it. If you HAVE to have a studio - forget about it. If you HAVE to go from Monday to Wednesday - forget about it.
Not that some of those wouldn't be possible, but I think you get the point. You MUST be flexible. You should have pretty good luck IF you are going during a relatively slower season, IF you don't mind spending points on weekend nights (they are higher, so fill up slower), IF you don't care which resort you stay in and IF you are flexible on the size of accomodations. We just recently booked a 2 bedroom and a studio at OKW for a trip in late April with no problem. However, BWV only had preferred 1 bedrooms open, VWL had 2 bedrooms only.
Bottom line: it CAN be done IF you are flexible. And you may be surprised how DVC ownership changes how you plan! DH and I have found we have SO much fun planning how to spend our points, we have our trips completely planned out THROUGH our 2004 use year! It's something we never really did before just because we never had a reason to. Now that we have the points to use - and keep track of - it's fun to get out the book or pull up the DVC planner program and just play!
Hope that helps!