When this question was originally asked (September 21st 2012), it was not possible to make a last-minute reservation on the Deutsche Bahn site. However I have just checked again (8th January 2013), and it is now possible.
It should also be possible to book a CNL train three days in advance or less at Voyages-SNCF.com. I have just tried for a date in three days time and I can proceed to the payment page. My understanding of the Resarail system that powers the voyages-sncf site, is that it would not be possible to get to this page if it was not possible to book. The ticket delivery options involve picking up the ticket with your credit card at the station.
At Loco2 we currently use a system called Euronet, which is owned by SNCF and connected to Resarail, so tickets, prices and availability are the same, but there are sometimes differences in ticket delivery options, as seems to be the case with this journey. We can only offer posted tickets for this journey, meaning that they are only available to UK customers booking more than 10 days in advance. We will soon have the same ticket delivery options as Voyages-SNCF soon.
One more thing to note is that the CNL services are "Subject to compulsory reservation", which I think means that if the train is sold out then it is not possible to buy a ticket on the day (unlike lots of trains where you can buy a ticket without a reservation regardless of how many other tickets have been sold). I guess in general this is a good thing because it wouldn't be very nice to not have a seat or a bed for the whole night on a train!