If there was more room out there to extend the tees back, Wintonbury Hills might have potential. It would take a monumental toughening of the golf course that would kind of defeat its current allure to public golfers: a nice, user-friendly new course. The course can play extremely firm and fast and the greens could defend themselves pretty well, but that's about it. The bunkers are largely out of play and again, the golf course is simply too short.
There is a local public facility called Tunxis Plantation in Farmington that has 45 pretty mediocre holes. Theoretically, it would take blowing away 36 of the 45 and building a totally new 18. The courses there drain very well, for the most part; their greens are always pretty firm. I wonder...
Similar situations are present at at least two other locations in CT: at Blackledge in Hebron and at Lyman Orchards in Middlefield. Both have 36 holes and enough theoretical room.
The last thing option I can think of is Richter Park in Danbury. It's an 18 hole facility but is adjacent to a big forested area. Of course, the local tree-hugging society might not take too kindly to the idea of hacking away at the woods to build a proper practice facility and bring the golf course to US Open readiness.
And on top of all this, Connecticut isn't likely to receive an Open because it's too close to NYC and there's already Bethpage Black, which is probably better than anything someone could come up with. I guess I'll have to move in order to claim that my state has held a major.