Can't start Time Machine backups on Catalina Running OS X Catalina, I am unable to initiate backups of any sort from Time Machine. The target disk is an external drive with plenty of space (multiples of the space on the internal drive I'm trying to back up). Here's the UI error I get:



Digging in under the hood, I find console errors from backupd that look consistently like this:

Failed to create APFS snapshot with name
  'com.apple.TimeMachine.2019-11-17-174139.local' on volume
  '/System/Volumes/Data',
  error: Error Domain=NSPOSIXErrorDomain Code=28 "No space left on device"


However, there is space on this drive:



In case the cause was a file system error, I rebooted via Internet recovery and ran:

fsck_apfs /dev/disk1


and found no errors.

I tried to re-enable local snapshots, but it appears that command is no longer available in Catalina:



Any idea how to get Time Machine backups running again?

note: This question seems similar to this question, which also does not appear to have a satisfactory answer.
As @Tetsujin suggested, the problem was indeed lack of space on the startup drive that I was trying to back up.

With 30Gb free, Time Machine was able to initiate a backup and stopped returning errors. (That is not likely the minimum limit; I just found something large and deleted it.)