Almost all (80%) of the latest "bulge" in M2 has come in savings deposits at large commercial banks, and this category is by far the largest component of M2 (see above chart). The Fed cannot force-feed money into savings deposits; people park money in banks only because they want to hold it, and that is especially true now that the interest rate on savings deposits is virtually nil. In other words, exceptional M2 growth in recent years has been almost exclusively a demand phenomenon, rather than a supply phenomenon: it's not that the Fed is running the printing presses in order to push prices up, it's that the demand for money has surged to unprecedented levels, and the Fed has been willing to accommodate this with generous supplies of bank reserves. Exceptional M2 growth has not sparked a big rise in inflation, because it has been the result of increased money demand. This may well change in the future, of course. If the demand for money begins to decline and the Fed does not act in a timely fashion to withdraw bank reserves from the system, then we could have an inflationary problem. This is one of the fears the weighs heavily on markets, and is likely one of the reasons that the price of gold has doubled since 2008.
This chart tracks money demand (the ratio of M2 to GDP). Since the onset of the 2008 recession and subsequent financial panic, the public's demand for money balances has soared in unprecedented fashion, and to an all-time high. The M2/GDP ratio has increased almost 20% since the end of 2007; i.e., money growth has exceeded nominal GDP growth by 20% in the past four years. If the increased demand for M2 in recent years were to reverse without there being an offsetting decline in the amount of M2, this could eventually fuel an extra 20% increase in nominal GDP, and much of that could come in the form of higher inflation.
In fact, money demand has most likely already fallen from its peak, because annualized M2 growth in the most recent 3-mo. period has been only 2.6%, while nominal Q4/11 GDP growth is likely to be at least 5% (e.g., real growth of 3-4% and inflation of 1-2%). If the Eurozone crisis manages to morph into a non-catastrophic problem, then confidence will slowly return, money will come out of hiding and be spent (e.g., be withdrawn from savings deposits), and economic activity will almost certainly pick up. We could be in the very early stages of this process already.