Removing the drive belt from the drill press spindle pulley makes the chuck a lot easier to turn. Then use a pin punch in the chuck key holes as the tap gets harder to turn once the tapered part of the tap enters the hole and the full thread engages. On a blind hole, start with a plug tap, then go to a bottoming tap if you want a full thread to the bottom of the hole. I don't know if Heli-Coil taps come in the three standard types, taper, plug, and bottoming. I usually buy taper taps and grind them off to make plug or bottom taps. It would be very important to get a full cut to the bottom of the hole when tapping for a thread insert because the bottom few threads would tighten up the coil if a full-depth thread isn't cut before installing the insert. You'll only get one shot at doing it right.
Jerry