Another user found a fix. I tested it and it worked.
Go to your Documents folder, Create a folder called BioshockHD, then a folder called Bioshock in that folder, and a folder called SaveGames in there.
If you have set or changed the My Documents default Windows 7 folder on another destination (as i've done the first time: i have an SSD for system and apps and a 2nd HDD drive for all the otehr data), the game will not be able to find it and it will fail to create the BioshockHD\Bioshock\Savedgames folder on the C:\users\"USER"\my documents.... and then it will give you the 'not enough space' bug.
The solution here is to restore all the Windows 7 default folders / libraries and set the C:\users\"USER"\my documents as your default save location.
I can't say that it will solve the issue if you already have installed the game. Maybe it will require a new installation of the game.
