Story highlights Democrat Michelle Nunn has a small 47%-44% edge over Republican David Perdue.

That's according to a new CNN/ORC International survey

If Nunn wins, she'd be the first Democrat elected statewide in more than a decade

The gubernatorial race between Gov. Nathan Deal and Democrat Jason Carter is also close

Democrat Michelle Nunn has a slight 47%-44% edge over Republican David Perdue in the Georgia race for an open Senate seat, according to a new CNN/ORC International survey released Friday.

The three-point margin falls within the poll's sampling error of plus or minus four percentage points, meaning the two candidates are statistically tied less than two weeks before Election Day.

If neither candidate garners 50% of the vote, the race heads to a January runoff.

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Democrats are throwing a lot of money in Georgia, as the party hopes to thwart what's widely expected to be a strong year for Senate Republicans and their quest to take control of the Senate. The GOP needs to win a net six seats to win the majority.

Libertarian candidate Amanda Swafford is pulling 5% of the vote in Georgia, keeping Nunn and Perdue from reaching the 50% threshold.

A Libertarian candidate is also peeling off votes in Georgia's contested gubernatorial race between Republican incumbent Gov. Nathan Deal and Democratic challenger, Jason Carter, the grandson of former President Jimmy Carter.

The CNN/ORC poll, conducted by telephone October 19-22 with 565 likely voters, indicates Carter has a 48%-46% advantage over Deal, while Libertarian candidate Andrew Hunt gets 6% support.

In the Senate race, CNN Director Keating Holland said Nunn's ability to make the race competitive in a reliably red state -- no Democrat has won a statewide election in more than a decade -- is a surprising show of strength.

"The Georgia electorate appears to be the most pro-Obama group of likely voters in the 11 states CNN has surveyed this fall," Holland said. "That's not saying much -- Obama's approval rating among Georgia likely voters is only 44%. But that's still better than the high-30s he gets in states like Iowa and new Hampshire, not to mention the low 30s in Kansas and Alaska."

Nunn has a particular advantage over Perdue among likely women voters, 56%-38%, and among likely voters who live in the all-important suburbs that dominate much of the state's political scene, Holland added.

In a hypothetical runoff, Nunn still holds a small margin over Perdue, 51% to 47%. But the poll's likely voter model can only estimate the November electorate, as a runoff election can draw a smaller and different crowd than the general election.