The Galaxy Tab 7.7 (GT-P6800) has an update to Android 4.0.4 Ice Cream Sandwich available on Kies. Kies is a desktop application that you can sync and update your devices with. I am not sure why this is not an over the air update.
This does appear to only be available for the unlocked Wi-Fi + 3G model of the Galaxy Tab 7.7 and not the Verizon LTE variant. Samsung said that Ice Cream Sandwich would be coming to their tablet line in July and August and we are already seeing that start.
Source: Sam Mobile