This article is from the alt.usage.english FAQ, by Mark Israel firstname.lastname@example.org with numerous contributions by others.
These phrases mean "exact likeness". "Spitting image" is first
recorded in 1901; "spit and image" is a bit older (from the late
19th century), which seems to refute the explanation "splitting
image" (two split halves of the same tree). An older British
expression is "He's the very spit of his father", which Eric
Partridge, in his "Dictionary of Slang and Unconventional English"
(Routledge, 1950) traces back to 1400: "He's ... as like these as
th'hads't spit him." Other languages have similar expressions;
e.g., the French say "C'est son pere tout crache" = "He is his
father completely spat." Alternative explanations are "so alike
that even the spit out of their mouths is the same"; "speaking
likeness"; and a corruption of "spirit".
"There's a sucker born every minute"
Those of P. T. Barnum's acquaintances who mentioned the
subject were unanimous in insisting that he never said this. The
closest thing to it that can be found in Barnum's writings is:
"I said that the people like to be humbugged when, as in my case,
there is no humbuggery except that which consists in throwing up
sky-rockets and issuing flaming bills and advertisements to attract
public attention to shows which all acknowledge are always clean,
moral, instructive, elevating, and give back to their patrons in
every case several times their money's worth" (the Bridgeport
Standard, 2 Oct. 1885).
Captain Alexander Williams, a New York City police inspector
at the time, attributed "There's a sucker born every minute, but
none of them ever die" to Joseph Bessimer, a notorious confidence
trickster of the early 1880s known to the police as "Paper Collar
Joe". See "P. T. Barnum: the Legend and the Man", by A. H. Saxon
(Columbia University Press, 1989).
"There is a Sucker Born Every Minute" is the title of one of
the songs in the 1980 Broadway musical "Barnum" by Jim Dale.