Migration Assistant and USB Time Machine disk
I've had a similar problem, which may be different to your problem because all the computers in my house share the same backup drive, and so there are lots of different backup files. 

My problem (which I fixed) was that Migration Assistant couldn't see the backup drive, but it turned out that if I opened the drive in Finder, and then opened the '.sparsebundle' file that belonged to my computer, then all of a sudden the backup drive became visible to Migration Assistant and I could restore from backup.