Here are the fan approval ratings of each of the head coaches in the league. These are the current rankings as of this morning, as they are ongoing and vary as the year progresses, often widely early in the year.

http://espn.go.com/nfl/sportsnation/ratings

Belichick 90%
Smith, Mike 80%
Morris 80%
Reid 80%
McCarthy 80%
Cable 79%
Payton 75%
Mangini 72%
Ryan 68%
Coughlin 66%
Garrett 66%
Caldwell 63%
Sparano 61%
Tomlin 61%
Del Rio 60%
Fisher 59%
Gailey 59%
Carroll 58%
Smith, Lovie 57%
Schwartz 51%
Harbaugh 51%
Singletary 49%
McDaniels 41%
Spagnuolo 41%
Shanahan 33%
Kubiak 33%
Whisenhunt 33%
Turner 31%
Haley 30%
Fox 21%
Lewis 16%
Childress 6%