While the term and the concept it represents are both today rather obscure (a deficiency I hope to cure), the term did enter the popular parlance of the day rather quickly in the 1950s, only to fade gradually into the fog of history.
I recently came across this post from Opinio Juris, a blog about international law and international relations. The post's author, Professor Kenneth Anderson (of the American University Washington College of Law), quotes a passage from Have Space Suit -- Will Travel, a 1958 story by the great science fiction author Robert Heinlein and published two years after Haley's paper:
“Russell, I heard on your tape that you plan to study engineering - with a view to space.”
“Yes, sir. I mean, ‘Yes, Mr. Secretary’.”
“Have you considered studying law? Many young engineers want to go to space - not many lawyers. But the Law goes everywhere. A man skilled in space law and meta-law would be in a strong position.”
“Why not both?” suggested Peewee’s Daddy. ”I deplore this modern overspecialization.”
“That’s an idea,” agreed Mr. van Duivendijk. "He could then write his own terms.”
I suspect, but have no evidence, that Haley and Heinlein either knew each other, corresponded, or at least that Heinlein was aware of Haley's work. The latter is entirely plausible. We do know that Haley's presentation of his paper at the International Astronautical Congress in Rome in September 1956 was covered in the October 1, 1956 issue of Time.
In addition, Haley's presentation of a similar paper a few months later was covered in the December 29 issue of The New Yorker the same year. In this article, Haley explicitly claims, "It's something else to imagine laws suitable for beings that are themselves scarcely imaginable. The word I've coined for such a body of laws is 'metalaw,' which I define as 'the law governing the rights of intelligent beings of different natures and existing in an indefinite number of different frameworks of natural laws.' "
Even if Heinlein did not know or correspond with Haley, he may well have read about his work in one of these publications.