If you doubt that it is so common, just try a Google News search for the phrase.
Where does it come from? The Mavens' Word of the Day enlightens us:
Which is all very interesting, but this madness must stop.
What is most surprising about the common phrase a tad is how new it is. Though it seems the sort of slightly old-fashioned thing an elderly relative might say, it never really had much currency until recently.
An Americanism, the earliest relevant sense of tad was 'a small child, especially a boy'. It was also used jocularly of old men, but this was never the primary meaning. This sense seems to be first recorded in the 1870s, but there are some earlier examples, of unclear meaning, in college slang dating to the 1840s.
The more usual use of tad is the sense 'a small amount or degree; a bit', often used in the adverbial phrase a tad 'a little; slightly'. This is first recorded around 1940, but does not seem to have become common until around 1970. The two largest American dictionaries of the 1960s, The Random House Dictionary, Unabridged Edition and Webster's Third New International Dictionary omitted this sense. In our files we don't start seeing large numbers of citations until the early 1970s.
The origin of tad is uncertain. It is usually thought to be a clipping of tadpole, though it could also be a dialectal variant of toad (from which the first element in tadpole is itself derived), which has also been used as a humorous term of address for a small boy.