I have used the single mic method many many times.  The ONLY way this works is if the band is familiar with the dance required to mix themselves.  I always use another input for the bass.

Here is a blog post I wrote a while back concerning mixing bluegrass in general:

http://folksoundguy.blogspot.com/2009/08/mixing-bluegrass-and-old-time-string.html

And here is an exhaustive discussion on PSW that it spawned mostly regarding the one mic method:

http://srforums.prosoundweb.com/index.php/t/48660/473/

Here is a great example of group of musicians recording a song using a single microphone.

http://www.youtube.com/watch?v=Pl-WCsP3pZk&feature=player_embedded

Placing the mic at chin height may also create visual problems as the large condensor blocks the performers face.

An easy solution is to lower the mic to chest level and tilt the mic back away from the performers. This keeps the vocals on axis but lowers the level of the instruments be having them more off axis.

If you go back and review many of the early photos of performers like Flatt and Scruggs you will see the microphone is at an angle, not straight up and down.

My experience in the bluegrass world is that far fewer bands are opting for the one mic method than about 10 years ago when this was really back in fashion. Many bands that tour nationally have gone to a hybrid method where a couple of instrument mics are added to the center mic. Any band interested in this should carefully watch Del McCoury, Hot Rize, or Steep Canyon Rangers to see how well the movement around the mic is set up.

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