A poll from Democratic firm Public Policy Polling released Monday showed Chambliss could be vulnerable to a primary challenge. Only 38 percent of GOP primary voters surveyed said they wanted Chambliss to be their party's nominee, versus 43 percent who say they would prefer a more conservative candidate.

Of those surveyed, 24 percent said it was important to abide by the Norquist tax pledge, while 21 percent said it was unimportant.

The survey also found that if Republican presidential contender Herman Cain mounted an electoral challenge, he could edge out Chambliss. Cain was the choice of half of GOP voters in a hypothetical one-on-one match-up, compared to 36 percent for Chambliss.