(David Goldman / AP Photo)

Is Barack Obama on the ballot?

Who really cares about American jobs?

Why choose between Republicans and Democrats anyway?

Those were the questions at play in a lively Georgia Senate debate Tuesday night in Perry, where Democrat Michelle Nunn and Republican David Perdue squared off-with a rare appearance from a third candidate, libertarian Amanda Swafford, who joined them onstage.

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In an auditorium at Georgia's state fair, the candidates traded barbs over their records and the president's, each drawing enthusiastic cheers from a split crowd as the debate moderator repeatedly called for the crowd to settle down so the panel of questioners could hear the candidates' responses.

"I'm not sure he's recognized that he's not running against Barack Obama or Harry Reid-he's running against me," Nunn said of her opponent, making a case that she'll work across the aisle if elected to the U.S. Senate, telling audience members that collaboration is the best way to solve problems like the federal deficit.

"Michelle, I have a lot of respect for you, but you're dead wrong," Perdue responded. "I'm absolutely running against Barack Obama and Harry Reid. Make no mistake, no amount of false advertising can obscure the fact that Barack Obama handpicked you."

Some of Obama's policies were certainly on trial Tuesday night, and not just the Affordable Care Act, a staple of this campaign: "He created the vacuum that allowed the rise of ISIS" by not leaving a residual force in Iraq, Perdue charged, when asked about the terrorist army.

In mentioning advertising, Perdue touched on a major theme in the Georgia Senate race: intensely negative TV ads.

After Politico reported that Perdue said, in a deposition, that most his career was spent outsourcing manufacturing for American companies in Asia and elsewhere, Nunn aired an ad accusing him of outsourcing American "jobs." Perdue contested that claim as false on Tuesday, and he has said he's proud of a career scouting overseas manufacturing and that such activity is a common part of American business.

Perdue, for his part, aired an ad accusing Nunn of funneling money to terrorists. An internal campaign memo expressed fears that Republicans would attack Nunn's record running former president George H.W. Bush's Points of Light Foundation over grants to terrorists. An arm of that organization had facilitated donations to Islamic Relief USA, the umbrella international organization of which has reportedly been accused by Israel of funneling money to Hamas.

Both candidates raised those issues Tuesday night, Nunn calling Perdue's ad "shameful" and reminding the crowd that "his tenure of outsourcing took place over 40 years."

Perdue told the audience he has spent his career "saving and creating real jobs. Michelle Nunn's false attack will not change any of that."

In a rare appearance by a third-party candidate, Perdue and Nunn were joined onstage by Libertarian Amanda Swafford, who polled at 6 percent in an early-September Atlanta Journal-Constitution survey.

(David Goldman / AP Photo)

Swafford has a chance to play a spoiler in this race, if her share of the vote prevents either Perdue or Nunn from surpassing 50 percent. When she wasn't fielding questions on gay marriage or medical marijuana (she supports the legality of both), Swafford made the case that neither party has offered effective governing solutions.

The panel of questioners, journalists covering the race in Georgia, asked Wafford questions about the traditional Libertarian set of issues, and she responded in kind, raising issues like the private prison industry and domestic wiretapping-"How long did the NSA spying program go on?" Wafford asked, before the American people knew about it-while pitching herself as a small-government alternative to Republicans and Democrats.

"Have you really heard anything different tonight from these two parties?" Wafford asked in her closing remarks.