I think your best shot at a last minute Le Cellier is more toward the 36-48 hour point - about the time people are cancelling ADR's they don't want. I've been looking for a December lunch for a while, and then just randomly checking the next couple days to see what comes up. I haven't had one come up for the next day, but I have had them come up frequently for the following day (and I'm usually looking around noon, not first thing in the morning).
I did manage to get a lunch ADR for Le Cellier for December, so whenever you are going, don't give up until the last minute. If all else fails, and you are in the area, try for a walk in when they first open (just be sure you have a backup plan in mind in case you don't get in).