Hi Kate,
Welcome to Apple Support Communities! We understand that you're currently unable to create a Time Machine backup, and it sounds like it's unable to create a snapshot on the internal hard drive for some reason. To help us isolate the problem a little more, how much free space is currently available on the Mac at this time? If there isn't enough free space available, that could be what's causing the Time Machine backup to fail.
We also have some additional information about local snapshots in the resource below.
About Time Machine local snapshots
Please let us know what you find, and we'll keep working from there.
All the best.