Oh, but that's not the doing of the administration, you are giving them too much credit! 
The Federal Reserve is a private bank, has nothing to do with federal government, other than perhaps buying its services... 
True, but I suspect that the Fed usually has gone along with most policies of the administration of the day.
Also, a lot of the money doled out was under control of the government (not the domain of the Fed alone):
February 2009
$787 Billion Stimulus Package – Average Americans Bailout
February 2009
$275 Billion Stimulus Package – Homeowners Bailout
March 2009
$30 Billion Stimulus Package – AIG Bailout
March 2009
$15 Billion Stimulus Package – Small Business Loans
March 2009
$1 Trillion "Toxic Asset" Program – Banks Bailout
March 2009
$22 Billion Stimulus Package – Automakers Bailout