Nunn is tied with businessman David Perdue and Rep. Phil GingreyJohn (Phil) Phillip GingreyEx-Tea Party lawmakers turn heads on K Street 2017's top health care stories, from ObamaCare to opioids Beating the drum on healthcare MORE (R-Ga.) in the poll, conducted by Democratic firm Public Policy Polling, and holds narrow 2-point leads over Rep. Jack Kingston (R-Ga.) and former Georgia Secretary of State Karen Handel (R). That lead expands to 5 points — 41 percent to 36 percent — over Rep. Paul BrounPaul Collins BrounHundreds apply to fill Isakson's Senate seat in Georgia Joe Lieberman's son running for Senate in Georgia California lawmaker's chief of staff resigns after indictment MORE (R-Ga.).

The poll shows the race is likely to be competitive, though Nunn is still fairly unknown in the state — roughly one in five voters has a favorable opinion of her, with the same number holding an unfavorable opinion of her. Most of the GOP candidates have similarly low name identification — nearly half of voters don't have an opinion of each of the primary competitors.

Nunn's father, former Sen. Sam Nunn (D-Ga.), is still well-liked: 56 percent of voters have a favorable opinion of the longtime lawmaker, with only 12 percent viewing him disapprovingly.

President Obama's unpopularity will be a problem for Nunn, however. Fully 54 percent of voters in the state disapprove of the job he's doing, with 43 percent approving.

The automated poll of 520 Georgia voters was conducted from Aug. 2-4 and has a margin of error of 4.3 percentage points.