It appears that the name was originally Backhaus but could have also been
spelled Backhus, Beckhaus, Beckhus, etc.
I would suggest you contact the following researcher and work together:http://trees.ancestry.com/tree/1695148/person/24056048962
Ludwig (or Louis) was married first to a Louise (based upon passenger list)
Louise apparently died shortly after their arrival as he married again in 1884
to Sophie Lindenwerdel.
I highly recommend that you obtain their civil marriage record & application
and then based upon that find the church they were married in to see what
the church marriage record holds. At that same church, I would also look
for the first wife's (Louise) burial record and pray they listed where she was from.
I would also recommend checking the baptismal registers for the kids born
here to see who baptismal sponsors were. Also, check to see if the church
has confirmation records - especially for Lutherans or evangelicals they would
sometimes list when and where a child was born on their confirmation record.
Check Louise & William's.
You might also wish to look in Louis's church burial record too when he died in 1909.
Don't forget to look in German newspapers for Chicago for his obit which may
list where he was born.
You might also try probate eventually if the above doesn't indicate a town of birth.
I am not sure if there are military records on William Henry Backus; however, they
too might have recorded his exact town of birth.