Have some snapshots get written to your C: drive and fill it up? You can actually move the snapshot files. By the official Hyper-V docs, I don't believe you're supposed to be able to move the VMs without merging the snapshots first.

However, here's how I have done it successfully.

1. Shut down the VM. 
2. Search the drive for *.avhd files. These are the differcing files created when you create snapshot.
3. Cut-and-paste these to an  alternate drive with more space.
4. Open the configuration xml file for the VM. It will be in the \<VM Name>\Virtual Machines\ subdirectory and will have a name of <GUID>.xml (ex 1311F536-D654-4ECA-90A0-BD23D627C223.xml).
5. Make a backup copy of this file, and then open the original in Notepad.
6. In this file, you will see the path + name of the snapshot files you moved. Update the name and path of the files, and then save your changes
7. Restart the VM and merge that was failing for you before should restart.

Additional Resources:

Here are some articles on snapshots that  will better explain how these work behind the scenes.

Hyper-V / SCVMM: Why aren't snapshots (checkpoints) recommended as a backup method?

Hyper-V Snapshot Common Issues

Understanding Hyper-V Snapshots | Anil Desai's Blog

Virtual PC Guy's WebLog : Managing Snapshots with Hyper-V

Guys, thank you both for your answers. Here's how I wound up on this.

The first thing that came to mind was "clear space on the C: drive". As it turned out, I didn't have a page file or any other easy wins there (and about 12 GB of snapshot files to merge!). Unfortunately, it seemed like moving the files was my only option. 

Since it was a lab, I stopped Hyper-V services through Hyper-V admin console.

Then I searched for those .avhd files and found them in a subdirectory with a path that included the machine name, so no worries there. 

Then I found the funky xml file with the guid in the name. I searched for .avhd in that file, and found all the references to these files. Then I changed the paths to the files here....after I made a copy of course 

Finally, I saved changes, started Hyper-V servies, powered on the VM, and yeay, it work! 

Thank you Pete and Hans for your help!