It's an area where we may never get much more evidence. I like the single-origin hypothesis simply because I suspect Homo erectus had some sort of primitive language by the time it diffused out of Africa.
Surely you can see the problem here. IndoEuropeans and Semitics are both caucasions, meaning that the languages split within the span of time that caucasians have been walking around, i.e. within the last 12k and probably within the last 5 or 6k years. That isn't enough time to pull the language groups as far apart as they are. In fact, the only provable connections betewen IE and semitic groups are a few words which were borrowed within historic times, like Eretz/Erde/Earth. All of the common words which would have to be the same or similar if the two groups were actually related are totally different.