One way to get a sense of whether an expression is widely considered a cliché is to consult a number of different dictionaries of clichés and see whether they include it. I happen to have four such dictionaries, so let's walk through them.
From Christine Ammer, The Facts on File Dictionary of Clichés, second edition 2006):
hit the nail on the head, to To say or do exactly the right thing. This analogy dates from the early sixteenth century and has counterparts in numerous languages. It was a cliché by the time Henry David Thoreau used it in A Week on the Concord and Merrimack Rivers (1849): "He will hit the nail on the head, and we shall know the shape of the hammer."
From Nigel Rees, Cassell Dictionary of Clichés (1996):
[not listed, although there is an entry for the unrelated "hit the —— for six"]
From James Rogers, The Dictionary of Clichés (1985):
Hit the Nail on the Head. To say or do something just right: to arrive at the right conclusion. The Romans had a similar saying. In English the thought can be traced to 1508, when John Stanbridge put it in his Vulgaria: "Thou hyttest the nayle on the head." To literally hit a nail on the head is something not even the best of hammers always do.
From Eric Partridge, A Dictionary of Clichés, fifth edition (1978):
hit the nail on the head, to. To hit the mark; to guess or state correctly or accurately: current from C. 16; cliché in C. 19–20.
The majority view, then, is that "hit the nail on the head" is a cliché—and has been one for more than a century. English writers have used it since at least 1508, and equivalent expressions may also be clichés in several other languages, including Latin. To me, the most surprising thing that emerges from these various entries is the fact that people in both the UK (according to Partridge) and the United States (according to Rogers) sometimes use the expression to refer to someone's having arrived at or guessed the correct conclusion. I don't think I've ever heard anyone use "You've hit the nail on the head" as a way of saying "Good guess." But maybe I'm just not a good guesser.