http://tascam.com/product/dr-680/specifications/
Tascam says up to 32 gb. I would contact them and see what they have to say about that!
This has been discussed generally here before though I'm not sure if the question was asked specfically about the DR680. The issue, as I recall it, is that cards 32gb or less are apparently some kinda different read format that the bigger cards. That's why the bigger cards are designated SDXC or something like that. So no, I understand that the bigger cards aren't able to be read on machines that aren't capable of reading SDXC cards.
For more information, scroll down to the third FAQ:
http://www.lexar.com/support/sdxc-faqs EDIT: I'm going to add a caveat to the above response. micro SDXC cards are now available in sizes above 32gb. As you probably know, there are SD card adapters that allow microSD cards to be readable in devices that use SD cards. It's POSSIBLE, though I have no way of knowing for certain, that you might be able to get higher capacities using the microSDXC card inserted into an SD card adapter.
I have an SD744t which uses CF card media. I bought a CF card adapter to enable SD cards to be used in my 744t. I then bought a 128GB SDXC card and, inserted into the CF card adapter, my 744t reads the entire 128GB on the SDXC card without issue. However, I really don't know if the CF format is different than the SD card format, in order to accurately extrapolate my 744 situation over to use on a SD based device. YMMV.