The poll also found Chambliss leads other contenders regularly mentioned as possible challengers. He leads Rep. Paul BrounPaul Collins BrounCalifornia lawmaker's chief of staff resigns after indictment Republican candidates run against ghost of John Boehner The Trail 2016: Let’s have another debate! MORE (R-Ga.) 57 to 14 percent in a head-to-head match-up. Against Rep. Tom Price (R-Ga.), Chambliss is also the front-runner, leading 52 to 34 percent. Lastly, Chambliss leads former Georgia Secretary of State Karen Handel 52 to 23 percent.

A majority of Republicans who describe themselves as "very conservative," 61 percent, say they do not want Chambliss to win the nomination, while just 23 percent of Republicans who identify as conservative say they do. Cain leads Chambliss among Republicans who identify as conservative with 68 percent support to Chambliss's 19 percent.

The poll's findings come a few weeks after Chambliss indicated to a local Georgia radio station that he would be willing to ignore the anti-tax pledge authored by Americans for Tax Reform president Grover Norquist.

"I care more about my country than I do about a 20-year-old pledge," Chambliss told the radio station. "If we do it his way then we’ll continue in debt, and I just have a disagreement with him about that."

The comment provoked strong criticism from conservative Republicans, and shortly after, Erik Erickson, an influential conservative and the editor of the conservative website, made mention of a possible challenge to Chambliss. Erickson eventually decided not to run.

— This post was last updated at 12:58 p.m.