Last week, I too thought the Euro would fall like a brick as their many of their member countries economy is much worst off than the US.
But, now that you mentioned it, I think it has all to do with export trades for the US.
Like many other countries, the US Treasury probably stepped in each time the Euro falls too much against the US dollar, very much like what the Japanese do when the Yen appreciates too much for their trade exports.
As for stuffing currencies in mattress, take it from me that the smell of printing ink (if new notes) is overpowering and the notes are definitely not meant to be slept on : )