Zero Hedge has reported there was a roughly $6.5 trillion synthetic (duration mismatch) USD short as of 4 years ago, and this effective short has gotten substantially larger following a 4 year regime of the USD as a funding currency courtesy of ZIRP (zero interest rate policy). Any time a Euroland liquidity shortage threatens to collapse the system, the first thing to surge will be the USD as the global financial system scrambles for USD, as was seen in 2008.
With USD FX swap lines, the Fed is effectively propping up the Euro banking system. Two weeks ago European banks saw the amount of USD-loans from the Fed, via the ECB's revised swap line, surge to over $50 billion. According to Anthony Sanders in testimony to the Congress Oversight Committee, the Fed's swaps program could eventually breach the $1 trillion level, versus a FX swap line usage peak of $583 billion after the Lehman failure in September 2008 triggered a near financial system meltdown. The additional supply of USD during QE1 eventually worked to substantially weaken the USD index (UUP ETF), by roughly 20%. But even before the Fed ended QE1 in March 2010, USD demand was again surging as the Euro crisis worsened and fears of a double dip in the U.S. economy triggered a selloff in stocks that forced the Fed into more directly monetizing Treasury debt with QE2 from November 2010.

When the Fed wound down QE2 in June 2011, demand for USD began to rise again because the Euro sovereign/banking crisis was not getting better, it was getting worse.
As the funding squeeze on Euroland banks reached a tipping point, the Fed was again forced into pumping USD into the Euroland banking system through USD FX swap programs with the ECB and other major developed nation banks.
Thus while the consensus solution to calm the markets and restore a semblance of normalcy is for the European Central Bank (ECB) to act as the "lender of last resort"—that is, to print the Eurozone out of trouble, it is a shortage of USD, not Euros that is squeezing the Eurobanks. Consequently, all ECB efforts would be for naught unless the Fed is supplying enough USD to cover the Euro USD shortage.
With a jump in USD FX swap funding provided by the Fed, the ECB is lending money for as long as three years to Euroland banks against a much wider range of collateral than it accepted in the past.