OK, bad example.  The Euro cannot "physically" handle the job.  The stock and bond markets denominated in Euros do not have the necessary capacity.
I believe the Euro bond market might be larger than the U.S.'s.  I've heard that anyway, although I can't provide a link to any substantial source.  If so, it's kind of silly to say the Euro can't handle the job.  

The dollar is not all that important.  Everything could easily switch over to Euros or other currencies.  It will happen, but it will no doubt take many years time.