I found two different sources about the origin of this phrase. One source said it originated with tobacco , the other source says it was due to taking a bite that was entirely too big for one's mouth . Regardless of the origin of the phrase being due to food or tobacco the meaning today is that someone has agreed to do something more than they can handle.

Read about the origin of this idiom here . Fascinating! And disgusting... Today it has the same kind of idea - except without the actual fat to chew. (that's gross) It means to chat or engage in idle conversation. It's similar, or maybe exactly the same, to shoot the breeze.

Originating in the military, this slangy term began to be used during World War I and soon spread to civilian life. Several vulgar versions, such as chew someone's ass out, should be avoided in polite speech. HA! It basically means to rebuke harshly.