With a lathe -

  Grab a piece of 1/2" diameter brass rod about 3" long.  Chuck it up, turn the outside down true.  Now drill a hole about 1.5" deep using a chuck in the tailstock, just a hair larger than the OD of the tap shank.

Use a dremel with a grinding wheel (or a file, if you're a glutton for punishment), to put some flats on the tap, just above the cutting threads.  Make it a size that's easy to grab with either a tap wrench or a small ignition wrench.  

Without a lathe -

Very carefully clamp the brass stock in the mill vice, then drill a hole in the center of it (as close as humanly possible) just a tad larger than the tap shank.  Modify the tap the same as above.  

To use -

Drill your hole using a drill press.  Without moving the workpiece, table, or head, swap the drill bit for the tap holder.  Put the wrench on the tap and slip it into the chuck.  Hand tighten the chuck, then lower the quill, lock it in place, and start tapping!  

For holes to a specific depth, put a set collar on the drill bit shank, set the plunge depth on the drill press, and use the above procedure.  That way when you replace the tap holder with the drill bit, your depth is still correct.  Most blind tapped holes have a bit of fudge factor involved in their depth, anyway.  

The above method sounds like a royal PITA, but in actuality it isn't that bad, and once you get used to it, it becomes very fast.  You tap the holes straight, true, and best of all, you'll rarely break taps anymore.  Unless you get crazy and abuse 'em.  

The above method also works excellent for tapping holes that are drilled at an angle to the surface of the workpiece.  Drill the hole, counterbore, etc, de-burr, then swap in the tap holder and tap it before you change the position of the workpiece or head.  Works like a champ every time.  

Just my $.0134 (damn recession!)