The genetic studies so far have been based on mtDNA, which is almost purely matrilineal and probably not a good enough molecular clock for the purpose. (A nuclear DNA study would be nice, if a good-enough specimen is ever found.) Also, as this survey article indicates, the anatomical differences are far more pronounced in Europe than they are elsewhere, especially the Near East. There thus may have been a local "species gap" that didn't exist everywhere at once. The situation would have resembled modern ring species in birds and salamanders.
I think most scientists agree that at some point you have to have been able to interbreed with something to have been descended from it. The curious total lack of any evidence of interbreeding between modern humans and neanderthals is most problematical precisely in the levant in which moderns and neanderthals are known to have existed in close proximity for long periods of time and you'd figure interbreeding should have been very common IF it was possible.
James Shreeve's 1995 Discover Magazine article on the topic is apparently now being used in university courses in paleontology. You can get to the article by going to Discover Magazine's Search Page, clicking the Archive Search Engine, and searching on "Neanderthal Peace" for the year 1995.