My daughter is a dual citizen (Cdn/US). Although I as a Cdn can use my Cdn passport in the GE machine, my daughter can use only a US passport in the machine. However, she has only a Cdn passport. CBP told her she had no obligation to have a US passport, just a valid passport. She was born in the US and has a US birth certificate. I was curious if any other duals with US citizenship had successfully used their Cdn passport in the GE machine. So far, all the duals have just posted using their US passport (as instructed).
I seem to recall instruction in my NEXUS booklet said use the passport and not the card in the machine, but many of us have found the card works fine as it is linked to the passport.
My concern was that her lack of a US passport may mean the card does not work in her case, since the US considers only her US citizenship. As emcampbe said, the US doesn't acknowledge the Canadian passport for Americans.
So far, crossing unaccompanied, she was able to use a NEXUS machine, but those are either gone or on borrowed time.
I have not had occasion yet to cross with my daughter to see if her card would work in the machine as mine does, and did not want to ask her to experiment while travelling unaccompanied. I'm just keeping my eyes open for other people's experiences in the mean time.