Rooms will be available, but I agree with Norma -- humping your luggage while looking for a place will be a pain in the neck. I routinely show up on the spur of the moment and have no trouble -- but I have a car to leave my junk in while I walk around a couple of blocks.
If you're determined to do it, pop above ground at Lux Gardens and walk north on St Germain (downhill) until Rue Soufflot opens up on your right (you'll be able to see the Pantheon at the end of the street). Turn right, then take your first left. This will be either Rue Le Goff or Rue Sorbonne (same street, but there's a name change and I can't picture where).
There will be a slew of hotels on your left as you walk by the university. If you haven't found one by the time you get to Rue des Ecoles, hang a right and walk to the end. Lots more hotels along the way.
They're all mid-range and the area is great. You'll find a room without a doubt, but the potential walk is close to a mile -- maybe a bit less.
If you want to get one ahead of time, try either the Cluny-Sorbonne or the Quartier Latin. The first is more convenient, I like the second better, and I've stayed in most all around there at one time or the other.