Is he even renegotiating anything? If he tweets to the world that he's "putting the deal on hold", that doesn't mean the army of people who are working on it have been ordered to stop. His twitter followers are completely unrelated to the mechanics of the transaction.
Twitter's board would be nuts to do anything but ignore his public statements, as long as the gears continue to turn behind the scenes. As you say, he "wants Twitter".
How would you deal with someone acting like an idiot in this way, after they signed an iron clad contract? I think most people would politely ignore it, and keep on completing the paperwork. There is no leverage until the person that wants to exert it jams some kind of lever in the gears, and that is not done by tweeting stupid things to the public.