I actually have some sympathy for the Austrian argument that the Fed cannot taper, but not for their reasons. They wrongly focus on base money creation as the main problem. But as Aziz says, base money creation would have to be a) far more extensive and b) have a far more direct effect on broad money to result in the hyperinflation that they fear. The real risks come from the market effects of persistent QE.
Central banks have become the largest players in global markets. It is somewhat unclear as to whether markets respond to central banks or vice versa - it's probably a bit of both - but we really can't pretend that central bank actions have no effect on global markets. The Fed is the largest and most important central bank in the world. Its actions are critical to the operation of global markets. Prices along the yield curve are governed by market view of the Fed's likely future actions - often the wrong view, because the Fed's price signals are far from clear, despite its vaunted commitment to "forward guidance": to see just how conflicted Fed price signals can be, you only have to look at Bernanke's announcement of imminent tapering followed by delay after delay. There remains a high degree of uncertainty in the markets regarding the future path of US monetary policy, which makes markets unstable and over-reactive. It's as if everyone is in a state of "amber alert" - there is a hurricane coming, but we don't know exactly when or where it will hit or how bad the damage will be.
Exactly how QE affects the economy is a matter of considerable debate. Inflation expectations tend to rise when QE commences, because many investors still think expansion of base money = inflation. But there appears to have been little or no effect on consumer prices, and it is unclear to what extent asset purchases benefit the wider economy. However, the one thing we KNOW QE does is support asset prices - all classes of asset, not just government bonds and MBS. Global markets have become used to this support: investment decisions are now governed to a large extent by the desire either to avoid capital erosion on safe assets (hence moves into assets that give zero yield, such as cash - zero yield is better than negative yield) or find some positive yield somewhere.
Tapering is removing central bank support of asset prices. Unless not just the US economy but the GLOBAL economy is "on the up" at the time that tapering commences, the result of tapering will be a global fall in asset prices. That isn't going to cause hyperinflation, as the Austrian school thinks, but it would cause a global recession.
I'm afraid it is not US fundamentals, but global fundamentals that will determine the Fed's ability to taper. If the Fed tapers when the global economy is already in the doldrums, as it is at the moment, the recessionary rebound to the US economy would be considerable.
It would also in my view be highly irresponsible of the Fed to cause a global recession by ill-judged tapering. Because of the US dollar's pre-eminence (and the pre-eminence of USTs, too - we don't talk about that enough), the Fed is effectively the world's central bank. It is high time that the US accepted that its monetary (and fiscal) policies must be driven by the needs of the global economy, not just the US. The "exorbitant privilege" is an exorbitant responsibility, too.
Can the Fed taper? - Azizonomics
World Economic Outlook, October 2013 - IMF
The Ins and Outs of LSAPS - Krishnamurthy & Vissing-Jorgenson
Methods of Policy Accommodation at the Interest Rate Lower Bound - Woodford