Listening to the news this morning, I heard the following statement: " The hostage situation has left Britain with egg on its face". "To have egg on one’s face" means to be very embarrassed or made to look silly. There are various theories about the origin of this expression:

The first, suggested by the late John Ciardi, traces the phrase back to the days when discontented theater audiences routinely pelted substandard performers with household refuse, including overripe vegetables and rotten eggs. (…)

A more likely but less dramatic explanation would simply be that the phrase refers to traces of egg unknowingly left on a diner’s face after breakfast.

(from Word Detective)
World Wide Words offers a third explanation:

Occasionally, a trusted, working farm dog would develop the bad habit of taking eggs from nests and eating them, turning himself from asset into liability.

Make your pick!