To quote an awesome user who sent me this tip, that might be helpful if any of you run into trouble:
"Well I bet your busy the past few days with the release of the game on Steam! Anyways I had this problem after purchasing the game, it kept saying "Steam servers are too busy" try again later. It kept making me sign in again too, something about a steam ticket expiring. Anyways here is a thread to the solution, I just had to rename something called the ClientRegistry.blob file and restart steam and everything is smooth.
Anyways just in case other people have the same problem! Here is the link.
http://forums.steampowered.com/forums/showthread.php?t=873128"
