I asked him the same question a few days ago, and he was more hedgey, saying something like, "I don't think so." It sounds like he was more definitive with you.
Certainly business has not been good enough so far to warrant an extension, but I think it has a good chance of winning either 4 or 5 Tonys (it's nominated in 5 categories: revival, director, and for Mantello, Hickey, and Barkin), and I think business will pick up after the Tonys to some extent. It will probably win more Tonys than any other play (and possibly as many as Mormon).
But I would guess they would have to replace some of the cast (Parsons must have to start filming Big Bang Theory at some point in July), and it may be a situation similar to Red in which they will close the show rather than re-cast some of the parts. (Although one key difference is that Red re-couped prior to closing, and I doubt that The Normal Heart has made significant headway towards doing so. It's about halfway through its scheduled run, and it's only grossed about $1.48 million so far.)
"What was the name of that cheese that I like?"
"you can't run away forever...but there's nothing wrong with getting a good head start"
"well I hope and I pray, that maybe someday, you'll walk in the room with my heart"