So did you have any luck naming that bird? I heard a bunch of guesses, in person, on Twitter, via email, but not many correct answers. It is a tough one, especially at that distance. By far the most common response was some type of sparrow, such as Savannah or Vesper. Here is the same photo again...
Followed by a larger version of it...
Any thoughts now? Keep in mind this bird is on a beach and it was in the winter, thus you are seeing non-breeding plumage. This is actually the only realistic way you would see this bird in Connecticut since it does not nest here.
Here are better shots of the same individual as it fed.
Do you have it now? It is a Lapland Longspur. They are very difficult to spot in Connecticut sometimes, this winter being one of those times. With that said, one or two are seen usually at least a few times on Long Beach or Pleasure Beach in Stratford and Bridgeport, respectively, each winter season. Seaside Park in Bridgeport is another good spot, as is Short Beach in Stratford, where I saw a lone individual a couple weeks ago. The bird pictured above was on Long Beach on January 5, 2010.
The best way to find them, aside from walking through coastal dunes on a frequent basis, are to seek out the much more obvious flocks of Snow Buntings and Horned Larks, as they will often associate with them, even if only loosely. It might be an even easier time to pick them out right now since coastal Connecticut was buried in several inches of snow yesterday. Always watch any part of the uncovered beach or nearby areas where grass has been ripped up along with plowed snow for a variety of good birds.