My Grandmother told me this story that she had been told when she was a young girl. I was amazed to find that same story on a website about the Willard family! Here is the story:

Family's traditional story told about Martin Willard:
A farmer heard an unusual sound and realized the noise was that of a baby crying. A search revealed a baby in a willow basket, floating in a creek, tied to a willow tree with martins singing overhead. The baby appeared to be well fed and clothed and had only recently finished nursing a bottle which used a hollow quill for a niple. No parents ever came forward to claim this child and the unknown male infant was given the name 'Martin' for the birds singing in the trees and 'Willard' for the willow basket in which he was found. This family tradition is known to several descendants of Martin Willard. While so far it has only been indentified through descendants of Martin's son Joseph, some of these children were living apart more than 140 years ago. All of the versions follow essentially the same theme including the source of bothe the first and last names. None of them tell us when this event occurred or where it occurred. The family which raised young Martin Willard is also unidentified. there are variations and emblellishments to the story including a version which reports a ship sailing away in the distance and speculates of royal descent. This has the ring of something added by storytellers over succeeding generations to make the tale a bit more interesting. As might be expected, there is no evidence to support this tradition and it cannot even be said with certainty that it relates to this Martin Willard as distinguished from some still earlier Martin. This tradition has essentially two arguments for its acceptance as true. The first is that it is not the kind of story that one is likely to make up to conceal one's origins. It would have been easier to have simply claimed that one's parents died when he was young. The second argument in its favor is the failure to find any trace of Martin Willard prior to about 1765. At least two professional genealogist have researched the North Carolina archives in Raleigh, looking for a trace of the early Martin Willard and nothing has ever been located. Several amateurs have also sought clues along the eastern seaboad with nothing to prove or disprove this family tradition.