According to the Random House Historical Dictionary of American Slang this
humorous expression meaning any bad road dates back to at least l698. The
dictionary quotes a "doubtful" story about the term's origin told by a NYC
dentist: I was told as a child that Featherbed Lane got its name in the
Revolution. The story was that Washington was afraid his troops would make
too much noise marching through town at night, so to fool the redcoats he
got all the housewives to pave the roads with their featherbeds so the army
could move silently . . . Most likely the term refers to vehicles sinking
in a muddy road as if in a bed of feathers.