There are actually multiple types of 1" headset, the two most prevalent being the ISO 1" (the current standard) and the JIS 1" (more popular on older Asian bikes), so you may not have the right one. (Or you could have a 1 1/8" headset on the cruiser.)
All the fun and exciting details here -
http://www.sheldonbrown.com/cribsheet-headsets.html