Abrams Republican challenger, Georgia Secretary of State Brian Kemp, has held the lead and is expected to be declared the victor on Friday, charged that Abrams has led a "publicity stunt" and her refusal to concede the election serves as a "ridiculous temper tantrum".
Abrams and voting rights activists have argued for months that Kemp mismanaged the elections system as secretary of state, with Abrams often calling Kemp "an architect of suppression".
Attorney Vincent Russo, counsel to the Kemp campaign and deputy counsel to the Georgia Republican Party, and Ryan Teague who also represents the GOP, which intervened in the case before Jones, could not be reached Wednesday night. Ohio Senator Sherrod Brown said on Wednesday that if Ms Abrams loses it's because Republicans stole the election.
"We can no longer dwell on the divisive politics of the past but must focus on Georgia's bright and promising future", he said shortly after Ms Abrams' speech.
But in a fiery speech, Abrams insisted this was no normal concession, decrying the voter suppression - at the hands of Kemp, the former secretary of state - she believed had led to this conclusion.
"After all of the theatrics, the math remains the same", Kemp campaign spokesman Cody Hall said in an email.
This combination of May 20, 2018, photos shows Georgia gubernatorial candidates Stacey Abrams, left, and Brian Kemp in Atlanta. "This election is over".
"In the coming days, Fair Fight Georgia will be filing a major federal lawsuit against the state of Georgia for the gross mismanagement of this election and to protect future elections from unconstitutional actions", it continued.
The odds aren't in her favor; Abrams needs enough votes to pull Kemp under 50% of the vote to force a runoff and the recounts haven't provided almost enough uncounted ballots.
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Kemp is leading with 50.23 percent of the vote to Abrams' 48.83 percent.
The order stems from a request in a lawsuit filed on Sunday by the Abrams campaign.
Abrams was considering further legal challenges as recently as Friday morning, but ultimately made the decision to end her campaign in a fiery speech to supporters at her headquarters in Atlanta.
He declined to extend the period during which evidence could be submitted to prove the eligibility of voters who cast provisional ballots.
US District Judge Leigh May ordered Gwinnett County election officials on Tuesday not to reject absentee ballots just because the voter's birth year is missing or wrong.
Cox said courts must attempt to apply a nonpartisan standard of "doubt" to the election. Voters were denied a ballot and turned away from the polls because they hadn't voted in the last three years and/or the last two federal elections, and Kemp's office had purged hundreds of thousands of people from the rolls for "inactivity".
He said that would allow preparations to begin for any run-off contests, including those already projected in the races for secretary of state and a Public Service Commission seat.
"After we confirm that counties have complied with the judges' orders and sent to the Secretary of State all required documentation, we will commence the regular process of reviewing this documentation in a manner that ensures accuracy and compliance prior to state certification".