Update: the demo appears to be working as normal.
Update: reader Marc has uncovered a method of getting around the current Steam issues, which we've confirmed as working:
"When you click on download you can go forward by pressing cancel before the green loading bar jams and says servers are to busy, this will give you the ability to download the game and play it ... Only ONCE !!"
Update: user Gangsta692 points out below the demo is borked on Steam, which is currently experiencing issues; Rebellion says it's working now with Steam to resolve the issue and will also try to get it out on alternate outlets.
Recently console players got a taste of upcoming shooter Sniper Elite V2, and now PC players get their chance as well. Simply hit the source to download the demo via Steam.