Similar issues of back up hanging. Mine got stuck at 38% many times in a row on galaxy S4 and also my wife's phone.
To fix this, I went into the smartswitch main menu (the screen that appears when you start up smartswitch, clicked on "more" button at the top of that screen, and selected reinstall device driver. After doing that, the next backup was normal, although you do have to allow the time to back up 10GB, 20GB or more if you have a large SD card that is part of the backup.... that does take time.
Once it worked, in my case, it quickly got to 96%, then was on 96% for 20-30 min while saying "backing up messages" and the whole thing took about 45-50 min-- then finally completed (for about 20GB overall between phone and card). If your harddrive is churning away, even if the bar is not moving (but you see the pulse from left to right inside the bar), its probably working on the backup.
FYI, I had also removed all Verizon Backup Assistance programs on my computer and when I start the backup program, I have to click cancel on pop ups for Verizon Backup assistant asking if I want to download the program (don't!). Just click cancel and cancel and your smartstart program will reconnect with the phone and do its thing. You don't need the Verizon software.