Can you grab the cloud_log.txt file from the logs subdirectory of your Steam directory and put it up here as a Gist? That might help us diagnose.
We'll need more information to proceed.
I apologize...I apparently didn't have my notifications going to the right place. I was able to track this down to a firewall issue, so I am closing this out.
Nothing extracted yet.
I am unable to sync any of the current games I have installed in Windows that I have also installed in Linux (and played in Linux). Games I've tested that fail so far:
Each of these games shows the "Syncing" text next to the game when launching, sits for a minute, then pops up an error stating that it has failed, asking if I'd like to play anyway or not.
Splice and Super Hexagon (which I don't believe I've played in Linux...if they even have Linux versions) both have showed the Syncing text after quitting, but then appear to have synced correctly.