maxrobert's observation helped me with this problem. During a repair by Apple my MacBook Pro's disk was wiped. I tried to restore to the Time Machine backup I made just before taking it in for repair. After getting the laptop back, my attempts to restore were stalling on the "Loading backup..." popup in the Migration Assistant when I attempted to restore. Using Cmd-R and restoring from Recovery mode wouldn't work either.
A look at the laptop showed that Apple had rolled back the OS to the original version of Sierra. I had done the backup with the latest version of High Sierra.
Instead of attempting to restore, I set up the laptop as a new installation I applied the OS upgrades necessary to get to the latest version of High Sierra. With that in place, I did a Cmd-R boot to Recovery Mode and did a Restore from Backup successfully.
With the OS upgraded to the version I had used for the backup the Time Machine restore worked as it should.