Netflix unavailable fix: clear Netflix cookes in your web browser
Not sure why this would cause the problem, but a (temporary at least) fix seems to be nuking any Netflix cookies currently set in your web browser.
In Google Chrome, click on the "customize" bars at the upper right, then "Settings," then "Show Advanced Settings" at the bottom, then "Content Settings ..." button (they don't make this easy!), then "All cookies and site data..." button (almost there!), and finally look for every cookie with "netflix" in the address and delete it. Click "Clear browsing data" on the way out just to be sure, restart Chrome and Netflix should let you log in.
In Internet Explorer, Tools : Internet Options : Browsing History - Settings : View files will pull up a similar list. (Or you could just get draconian and tell IE to Delete all your cookies under "Browsing History."
Still not sure why local cookie settings would result in the "Netflix site unavailable/engineers working on it" message. Or why they couldn't post some helpful tips (like this one) instead of an unhelpful message.
Frankly, piss-poor customer service! I thought Netflix was better than this!