Hi!

Does anybody know what size power supply I might need for a typical
cordless drill motor?

It depends largely on what you expect the motor to do. What kind of a load
are you going to put on it?

The harder the motor has to work, the bigger of a power supply you'll need.
Voltages should be close but don't necessarily have to be exact.

I called DeWalt and the technical support person wouldn't tell me (I
think for liability reasons). He said that people have tried to use a
car battery to power a dewalt drill and something exploded or went
haywire on them.

If properly set up, that would work just fine. I could see the biggest
problem coming in the form of short circuits or poor wiring. A car battery
can produce huge amounts of current for a long enough period of time to
cause impressive damage. Some people who have tried this probably didn't
fuse or otherwise protect the circuit...which works fine until something
goes wrong! Then something might go "bang!" or worse.

William