It turns out the solution is relatively straightforward:
cat /dev/zero > /private/tmp/junk; rm /private/tmp/junk
The first part of the command will keep enlarging a file with zeros until disk space runs out. After an error, the second part will delete the empty file. Lather, rinse, repeat for extra security (7-pass, 35-pass Guttman).
[robg adds: I haven't tested this one...however, I'd be somewhat cautious about using it on your boot drive. Running out of space on the boot drive -- even briefly -- may cause issues. If you know more about that possibility than I do, please comment!]

