Hi Wally, 
Stephen Oppenheimer cites 
Bailliet G, et al, Founder mitochondrial haplotypes in Amerindian populations. American Journal of Human Genetics. 55:27-33 (1994).
Torroni A, et al, A mitochondrial  DNA "clock" for the Amerindians and its Implications for timing their entry into North America.  Proceedings of the National Academy of Sciences USA.  91:1158-62 (1994).
Forster P, et al, Origin and evolution of Native American DNA variation:  A reappraisal. American Journal of Human Genetics. 59: 935-45 (1996) 
and many more. I haven't read any of these source documents. This is why I only cited Stephen Oppenheimer's book "The Real Eve" Carroll & Grapf, NY, 2004  in which Oppenheimer outlines and discusses the relevant data and competing perspectives on this issue. It is also why I added "I am persuaded by the evidence offered by Oppenheimer. Others may not be."  

I think that the genetic evidence is powerful and persuasive. I am aware that many archaeologists cling to the idea that Amerindians arrived over the land bridge at Bering Strait following the last glacial retreat around 11,000 years ago.  They cling to this perspective despite the problems posed by several growing bodies of information. For instance, carbon dating has proven problematic, as many artifacts have been found in the Americas that predate this by very large margins. But, in my mind, the evidence derived from the mutations of mitochondrial DNA rang the death knell for this perspective.

I would encourage you to read chapter 7 from Oppenheimer's book to have a full appreciation of his argument and the supporting evidence. 

Best Wishes, 
Ron   

Wally Said: 

Ron, would it be possible to provide references for this? I recall seeing similar numbers a few years ago, but they were subsequently dismissed as inaccurate. The best reliable numbers I can come up with now is 12,000 - 15,000 (in North America).