They certainly have kept it under wraps. The new trailer showing what looks to be smaller monsters or.. something.. is intriguing.
I will make a prediction that we never actually see the creature or force or whatever it is that can apparently knock (not blow or shoot) the head off the Statue of Liberty and send it careening into the city. What we will see will be the reactions of people to the effects of this invasion. Abrams has said it's not a Godzilla film, so... that leaves precious few things I can think of that wouldn't resemble Godzilla to a great degree. Cthulhu is a popular guess, but I think that's too outside the box, here.