A few points here...the Fed only purchases Treasury securities from Primary Dealers (select large banks). They do not purchase anything directly from the US government. Therefore, any currency used in the purchase goes to banks - not the government.
A great majority of funds issued from Fed purchases of Primary Dealer securities stays in the Primary Dealer accounts at the Fed. It is not being circulated back in to the economy. This can be very easily seen by looking at Section 8 of the Fed's weekly H.4.1 report, which shows its balance sheet. You can look in the Liabilities area and see that "Term deposits held by depository institutions" is currently sitting at around $2.14 trillion dollars (from the 7/18/13 release).
Debt is "money" in a debt-based economy. "Currency" (both physical and electronic) is what is used to transact business - and is backed by debt.
“A few points here...the Fed only purchases Treasury securities from Primary Dealers (select large banks). They do not purchase anything directly from the US government. Therefore, any currency used in the purchase goes to banks - not the government.”
The dealer gets a cut, and although the funds may temporarily sit in accounts, the funds are not permanently under the control of the banks. The funds are eventually spent as directed by law by the legislative branch