The Steam Community has been chronically unreliable tonight. Unfortunately this is a regular occurrence and isn't related to the release of Borderlands 2. Valve needs to put a LOT more effort into minimising downtime - so many games rely on it to provide multiplayer and people are kicked out immediately if they lose the connection.
I would go as far as saying that the Steam Community isn't fit for purpose at the moment. Players are already posting about how they've lost 5 or more levels because of the disconnects. There were over 100,000 people online when it went down and a decent percentage of those would have been playing co-op.