Epic!
Well the easiest thing I could think of is a stand mixer, it's only about (depending on the model of course) 300w or so, but is geared so low that it has enough torque to easily push the drill and at a very safe speed (eliminating the need to excessively balance the 'bit'

, plus most have a nice shaft w/ a threaded ole to easily attach just about anything to... (and adjustable speed should an idiot spill their drink on you

)... Still gotta plug it in though...
As far a DC motor goes, taking the motor/gear box out of a power wheels (kids electric car) should have again, enough torque, and be geared low enough so you dont have to mess w/ gearing. the easiest thing would be to build the "bit" out of some flashing rivetted into a cone w/ more flashing for the blades, and attach it straight to the plastic wheel ripped out of the car... plus most are 6v or 12v, and run off batteries the size of my fist...
After reviewing the video, I'd probably go for the old power wheels drivetrain... less bulk to hide, plus portability (helluva lot lighter)...as long as the 'bit' section isn't enormously heavy I don't see why it wouldn't work, you could whip up a simple frame to mount it to slide the battery in, plus a push button switch , and a handle and have everything functional internal in the drill
Dude, you'd better post pics when you're done!