The expression “to bite off more than one can chew” means to attempt more than one can accomplish; to try to do more than one has time for, or the ability for.
A very human failing; one that is often quite praiseworthy, but also one that is often quite exasperating.
The former could be said of a student, for example, who, in the laudable desire to learn all he can, takes on more courses than he can find time to keep up with, and thus flunks several.
The latter could be said of my more-than-willing yardman, Lou, who cannot say no to anyone seeking his services and, accordingly, never turns up at an appointed date.
The homely American expression has been traced back some seventy-five years, but is undoubtedly much earlier.
It could have had a literal beginning with a small boy who took such a big mouthful as to be unable to do more than roll it around in his mouth; but more likely it started with a greedy person, say a Scotsman, who, borrowing a plug of tobacco, bit off too big a chunk to enjoy. (P.S. Lou isn’t with me any more.)