I think JustinC has given you a very good overview of the the relevant processes. Populations can only diverge to become separate species through accumulation of sufficient genetic differences. Population-level genetic differences can come about through various mechanisms, but most will be very muted in this case.
The founder effect will be reduced because of your relatively large initial population size (few alleles will be absent that are present in appreciable frequencies in the ancestral population).
If your population has technology to assist survival, natural selection will be a weak force for altering allelic frequencies as a function of local ecology and environment, wher it could be important for normal animals lacking technology.
We are left with really only two plausible scenarios for generation of a reproductive barrier: mutation and genetic drift. As pointed out by Sasquatch a single 'critical' mutation could accomplish the reproductive barrier immediately - but first it would have to rise to fixation within the population (become the dominant allele or genomic form). This means it would have to confer some strong survival or reproductive advantage. Not impossible, just a very low probability event and extremely difficult to predict if, when, or how long it would take to occur.
One the other hand, genetic drift is a sort of slow, inexorable process - isolated populations just gradually become genetically different purely by the chance survival /loss of alternative alleles. The speed that this effect will result in meaningful genetic changes between two isolated populations will be a function of various factors, particularly mutation rate, effective population size, and generation time. Two large populations with low rates of mutation and long generation times (like humans) could well take thousands of years to diverge in any way that could result in reproductive incompatibility - which isn't to say that it couldn't happen either.
The issue of cultural isolation brought up by clpmini is also an interesting point, because it is a far more plausible barrier to gene flow than geography in modern human society. Nevertheless, we know that only very low levels of gene flow are required to prevent genetic drift between populations, so the culturally isolated population could tolerate very few, if any, defectors and accept very new initiates for them to continue to drift away from the rest of humanity in genetic composition.
Hope this helps. EZ
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