A couple of weeks after I discovered the bird nest, one of the cowbirds hatched.
Jim discovered that if you whistled, it would open its mouth for food.
The second day, the other cowbird hatched.
I wish this story had a happy ending, but it doesn't. :-(
The third day, Jim noticed the babies were gone. By the time I came home, the nest was completely empty. I did a Google search and learned that birds don't/can't move their eggs, so most likely a predator got them. One of the pages I read saw that crows and hawks will take eggs, and we have both nearby.
What a bummer. :-(