As far as I understand, the ability of the Fed to do QE (and as an aside, the kind of repo rescue operations that happened last week) is dependent on US banks holding treasuries which can be exchanged for fed reserves. When banks aren't holding any more treasuries or the Fed has bought them all then QE has to end (please correct me if I"m wrong).
Given this assumption, my question is, do we know exactly how many treasuries are held by US banks, and if so, what is that number and how is it determined?