Booted up a VM into the SCCM OSD WinPE, entered password, and selected a task sequence. Before any packages were downloaded, I was hit with error 8007000E. The smsts.log file reports this error, and using the Trace Log Tool's error lookup that code means:
Not enough storage is available to complete this operation.
The VM's hard disk is IDE and 60GB Dynamic. I've never had this problem before.