Pass the buck
Evade responsibility by passing it on to someone else.
Look up 'buck' in the dictionary and you'll find a couple of dozen assorted nouns, verbs and adjectives. The most common use of the word these days is as the slang term for the American dollar. That's not the buck meant here though. Look a little further down the list and you'll find the definition 'buck: an article used in a game of poker' - and that's the buck that was first passed.
Poker became very popular in America during the second half of the 19th century. Players were highly suspicious of cheating or any form of bias and there's considerable folklore depicting gunslingers in shoot-outs based on accusations of dirty dealing. In order to avoid unfairness the deal changed hands during sessions. The person who was next in line to deal would be given a marker. This was often a knife, and knives often had handles made of buck's horn - hence the marker becoming known as a buck. When the dealer's turn was done he 'passed the buck'.
Silver dollars were later used as markers and this is probably the origin of the use of buck as a slang term for dollar.
The earliest citation that I can find of the literal use of the phrase in print is from the Weekly New Mexican, July 1865:
They draw at the commissary, and at poker after they have passed the 'buck'.
This is clearly around the time that the phrase was coined, as there are several such printed citations in the following years.
The figurative version of the phrase, i.e. a usage where no actual buck is present, begins around the start of the 20th century; for example, this piece in the California newspaper The Oakland Tribune, from May, 1902:
[Oakland City Attorney] Dow - 'When the public or the Council "pass the buck" up to me I am going to act.'
The reporter's use of quotation marks around pass the buck indicate its recent coinage as a figurative phrase, or at least one that the paper's readers might not have been expected to be familiar with.
The best-known use of buck in this context is 'the buck stops here', which was the promise made by US president Harry S. Truman, and which he kept prominent in his own and his electors' minds by putting it on a sign on his desk.
See other phrases that were coined in the USA.