Ken talks about the origin of "spitting image" here
I would like to add that there is a similar portuguese expression "cuspido e escarrado" that is used in the same way as "You are the very spit of your father": "És o teu pai cuspido e escarrado". The verbs "cuspir" and "escarrar" both mean "to spit", but "escarrar" is muckier and much more disgusting. The meaning of the sentence above is someting like " You are your father [made by] spitting. "
This expression is mostly used to point a resemblance between father and son, so I guess that what we are talking about is not spit, but semen.
I hate smilies!