This is the original recipe from the 1887 printing of the White House Cook Book by Mrs. F. L. Gillette, made available through Project Gutenberg.
Wash and quarter three or four good sized squirrels; put them on, with a small tablespoonful of salt, directly after breakfast, in a gallon of cold water. Cover the pot close, and set it on the back part of the stove to simmer gently, not boil. Add vegetables just the same as you do in case of other meat soups in the summer season, but especially good will you find corn, Irish potatoes, tomatoes and Lima beans. Strain the soup through a coarse colander when the meat has boiled to shreds, so as to get rid of the squirrel’s troublesome little bones. Then return to the pot, and after boiling a while longer, thicken with a piece of butter rubbed in flour. Celery and parsley leaves chopped up are also considered an improvement by many. Toast two slices of bread, cut them into diced one half inch squares, fry them in butter, put them into the bottom of your tureen, and then pour the soup boiling hot upon them. Very good.