Public Policy Polling released a survey Thursday that shows only 14 percent of Carolina fans want Davis to be fired.
Fifty-seven percent prefer he continue as the coach, while 29 percent have no opinion.
Forty-one percent of fans approve of Davis' overall job performance, while only 20 percent disapprove.
UNC's football program has been under investigation into improper benefits and academic misconduct since the summer.
The scandal led to the resignation of assistant coach John Blake.
UNC's student newspaper called on Davis to leave after this season -- saying he either had direct knowledge of major problems or was egregiously ignorant.
Davis has said he will not resign, and he has gotten support from the UNC Board of Governors, the chancellor and Athletic Director Dick Baddour.
Full poll results are available at: http://publicpolicypolling.blogspot.com/2010/10/overwhelming-support-for-davis.html