I did a search on http://dockets.justia.com/ for filings under chertoff between Jan 2006 and April 2007 and came up with 1800 for all federal courts.
Assuming some of these are not name check related (very small number possibly) and others may have been missed due to other indexes ie name check cases other than under chertoff, it is a goo estimate that there are around 1500 to 1700 cases filed between Jan 2006 and April 2007 on the name check problem. From Ombudsman page it looks like about 200K+ are stuck in name check, so it is safe to assume 10% of the stuck people out there are filing. If this percentage goes up to say 50% , Federal Courts will be swamped.
Also another number from my AUSA: only 100 cases per week from all country are getting expedited.