No, it's not just you. It's everyone. Steam is well and truly down. This is what it looks like when millions of players online suddenly drop to none. No matter how much you want to try the XCOM demo, it looks like you'll just have to wait.
We've reached out to Valve to find out what's going on and when Steam service is expected to be restored; we'll update when we hear back.
Update: The Steam Facebook page has been updated to say that its routine morning maintenance "is taking longer than expected".
Update 2: And we're back! Service was restored after roughly an hour. Go forth and game.
And just for fun, here's what it looks like when Steam comes back from being down: