Hard to tell since we really don't know how many consoles Microsoft planned to produce and how many they really produced. They could ship 1,5m in North America + the European markets but they could also only ship 600k or something like that.
If they could ship 1m day one in USA i would say maybe the first week but i really doubt that so probably end of December. But yeah, those numbers are all not really based on anything except for "as long as they ship so many"