I think the 1 month T-bill has been so low because some money managers have nowhere else to park their funds right now:
Here is the Treasury yield curve for the last 5 trading days: 1 month: 1.16, 0.71, 0.26, 0.37, 0.67 3 month: 1.11, 0.92, 0.61, 0.63, 1.24 6 month: 1.31, 1.32, 1.22, 1.20, 1.60 12 month: 1.32, 1.40, 1.33, 1.33, 1.68 (http://www.treas.gov/offices/domestic-finance/debt-management/interest-rate/yield.shtml)
It seems clear enough that the Fed Funds rate is not the only determining factor in what the 1-month T-bill does.
--tim francis-wright