See a detail of the lower right quadrant of the picture, showing nest, snake, and eggs at http://www.pbase.com/image/160182219 . In this full image, you can see the male (rear) and female parents watching as the snake, having invaded the nest, takes one of the eggs in its mouth.
Though the close-up shows the snake with the egg in its mouth, I never saw it break any of the eggs by biting. I later learned that these snakes swallow the eggs whole, break them open internally and digest the contents and some of the shell, and eliminate the rest of the shell.
Next full image, showing American Avocets on nest: http://www.pbase.com/image/160182192 .