We need to change the Endnote temporary citation format ([!Author, Year, Label!]) to BibTeX (\cite{Label}). I feel certain that there's a way to do this using Endnote, but I chose to write a Python script, texref.py, to do the job instead. Running the script gives you something like this:
texref.py document.tex Found 9 references in 6 citations. Backed up "document.tex" to "document_021107-1304.tex" Writing document.tex with modified citations.
document.tex now contains BibTeX formatted citations. No external data file is required, because all of the necessary information is contained in the Label field of the Endnote citations.