I know many have had this issue and I think one or two have pointed out the solution but I thought I'd create a new post so its easy to find for those who are having trouble.
I couldn't load FM via Steam from yesterday and again this morning, so I uninstalled FM via Steam but DID NOT delete the files in User/Documents/Sports Interactive so that I could keep my saved game.
That didn't work as every time I tried to re-download FM, Steam kept telling me the servers were too busy.
All you need to do is first delete FM via Steam, then remove Steam itself from your computer (I am using a Mac, not sure if this works on Windows but I assume it will)
I then re-downloaded Steam and when I did it auto-updated itself...before I uninstalled Steam, I tried to update Steam itself and it said it was up to date but then updated when I re-installed.
I was then allowed immediately to download FM again and it ran first time...and I didn't need to download my saved game which I noticed a few people have
Perhaps a Steam update and the FM update somehow conflicted...I don't know, I'm not a whizz on these things, but it's working now.