We found that if you continue to refresh the product page, eventually the "Coming Soon" will become "Add to Cart", but we were still having issues where once we hit the "Add to Cart" button, the phone wouldn't go into the shopping cart. This happened mostly in Google Chrome. However, we gave it a shot with Mozilla Firefox, and while there were still issues with disappearing items, Firefox did eventually work.
We had been suspicious of the claims that the phone was sold out, because usually a sold out device page will say something like "available in 2-3 weeks", not "Coming Soon", and it seems our suspicions were right. The Nexus 4 is not yet sold out, and if you want one, just fire up a couple different browsers and keep hitting that refresh button.