For background on the Cyprus banking crisis that emerged over the weekend, see here and here and especially these two posts from Pawel Morski. But back up and superficially at least the issue here is that Cyrpus needs 5.8 billion euros more than "the Germans" (some of whom in this case seem to be Finnish) feel like ponying up. So suppose Ben Bernanke is looking at financial markets and decides it would be perverse for there to be hundreds of billions worth of stock market declines around the world for want of 5.8 billion euros. He could have the Federal Reserve print up some dollars to purchase 5.8 billion euros or (5.8 billion euros worth of Finnish, Slovakian, Austrian, Dutch, German, Belgian, and French debt) and then deliver the money as a gift to President Nicos Anastasiades and tell him his problems are solved.
Nobody needs to lose anything. Of course people might ask Bernanke what kind of precedent this sets, but he could just say it's really not clear. It was a weird situation, and Cyprus is freakishly small. You can't necessarily expect the same thing to happen next time, so who knows. Plus, he might get impeached over it.
But economically, what's the downside here? Would we see runaway price inflation in the United States if the Fed handed 5.8 billion euros over to the government of Cyprus to prevent the haircutting of bank depositors? It's difficult to see how that would happen. Would you see runaway price inflation in Cyprus? Again, hard to see. Now you probably wouldn't really "save" Cyprus this way anyway. Russian tax cheats or whomever it is who's putting money in these offshore Cypriot accounts are probably going to be looking for a new safe haven no matter what happens. So Cyprus will have to cope with that over and above whatever other problems are afflicting it. But obviously Cyprus is better off with the present. And while I don't believe the hype about contagion to Portugal, Ireland, Italy, and Spain, the Fed bailout clearly makes contagion less likely so the Portugese, etc., are happy. The Germans (and Slovaks, who've been itching for a fight since Greece) will be superficially upset that they lost their chance to deliver some Old Testament justice, but it's difficult to see how they've lost out here.
The euro might move up against the dollar (back to where it was a month ago, say) rather than moving down in the bailout scenario. But I'd judge that as good for the U.S. (exports, and all that), as well as a nice vote of confidence in the European Project.
Of course it "sounds crazy," so it won't happen, nor will the "even crazier" alternative of Secretary Jack Lew minting a $8 billion platinum coin and mailing it to Nicosia. But it seems like a fine idea nonetheless.