Hi krregt!
Believe it or not, it could be even one damaged file or directory jamming the process up.
It sounds like you’ve already followed this:
If you can't back up or restore your Mac using Time Machine:
https://support.apple.com/en-us/HT204157
So if that’s the case, I just gave a few questions:
Were you able to backup before on the same external drive before this started happening?
If so, what changed from when it was working, to not working?
Can you say the available storage of the external and internal HD’s?
Apple > About This Mac > Storage.
Likewise, do you use this same external drive for other purposes, such as storage, etc. and do you use it on other machines? Whether Mac or PC?
And finally what’s the brand of the drive and how is it formatted?:
You can open Disk Utility to check, just press Command and the Space bar to pull up Spotlight Search, type Disk Utility and hit Return.
Next hit View > Show All Devices, can you post a screen shot after selecting the external disk and volume(s) of the external and even internal drives? (The disk is the top level, the volumes, or partitions are the underneath the disks).
Depending on those answers:
Are there other external hard drives connected to your Mac besides the one used for Time Machine? I ask, because Time Machine can also backup other external drives that are also connected to your Mac. (This might be a network drive, such as a Time Capsule or WD, if so just let us know).
Depending, you can exclude entire directories or files from backing up, such as system files and Applications, sometimes when this is done, it backs up just fine.
These options are available in System Preferences > Time Machine > Options. From there you can exclude files from being backed up.
Say it works fine after excluding Applications, (Or even one application or file), then the Apps, or this file is the cause of the problem.
There are a few directions to go, but I think knowing those answers is key to fixing it, cheers!