Actually, I tested something earlier, but I don't know if it's true or not. I had chosen to install Sonic Generations, but it wouldn't let me download from the servers due to them being swamped. I then immediately chose to install a different game, GTA1. Immediately, I was starting to download GTA1 from Steam's servers. Fascinating. Then I chose to download Sonic Generations again, to which I was declined again.
It might be a game-by-game basis. I didn't do enough testing to make sure, but I'll just assume that's how it works for now.
Sometimes you've gotta keep trying, even if it's the 10th or 20th attempt, the download will eventually pass through, it's happened with me even when trying to download one of the far less popular games. I found it's harder to start downloading a game when others on the same network are also downloading
or when you're also downloading other stuff. 90% of the time either one is the case for me.
Persistence is the key
But yes, it's harder to download during the Steam's massive sales, which the 'servers are too busy to handle your request', regardless, don't give up!