SAVANNAH, Ga. — Georgia's two Republican Senate candidates careened over the weekend toward a rocky end to their high-stakes dual runoff races, trying hard to avoid becoming collateral damage in a series of raging disputes that have embroiled the GOP.

Neither Sen. Kelly Loeffler nor David Perdue — whose Senate term expired Sunday — cast votes one way or the other on Friday when the Republican-led Senate handed President Trump his first veto override. Perdue and Loeffler are facing challenges in Tuesday's election from Democrats Jon Ossoff and Raphael Warnock, respectively.

Both Loeffler and Perdue aligned themselves with Trump's call for $2,000 stimulus checks to be sent to Americans, even as the idea was blocked by Senate Majority Leader Mitch McConnell (R-Ky.), who likened it to "socialism."

Control of the Senate rests in the hands of Georgia voters in the Jan. 5 runoff election that will determine two seats. (The Washington Post)

And on Sunday, Perdue and Loeffler sidestepped questions about their role in an effort being orchestrated by some of their Senate GOP colleagues — in defiance of McConnell's wishes but in sync with Trump's quest to overturn his election defeat — to oppose certifying President-elect Joe Biden's electoral college victory when Congress convenes Wednesday for what is typically a ceremonial act.

"I'm looking very, very closely at it, and I've been one of the first to say everything is on the table," Loeffler said during a "Fox News Sunday" interview, repeatedly dodging questions from host Bret Baier about how she would vote.

Perdue, appearing on Fox News's "Sunday Morning Futures," said he would not be eligible to participate in the Wednesday vote because the results of his runoff would not be certified in time. But he suggested that he would be on board with the idea if he could be there.

Republican senators continued claims of election fraud on Jan. 3, two days before the runoff election in Georgia. (The Washington Post)

"The technical problem is that I won't be certified until this election is certified some week to 10 days after the election, when we win on Tuesday," Perdue said. "But I'm encouraging my colleagues to object."

On the line in the remarkable twin runoffs is control of the Senate. If Ossoff and Warnock win, the Democrats would take control of the chamber, with Vice President-elect Kamala D. Harris casting the deciding vote once she takes office Jan. 20, making it easier for the Biden administration to enact its agenda.

Harris campaigned here Sunday, and both Biden and Trump are scheduled to headline rallies Monday in the closing hours of the campaign.

But the runoffs are ending just as the Republican Party is becoming increasingly embroiled in open warfare, presenting challenges for Perdue and Loeffler.

Especially contentious, especially in Georgia, has been Trump's increasingly frantic efforts to overturn his election defeat. Perdue and Loeffler have both echoed Trump's baseless claims of fraud in Georgia and other battlegrounds, calling for the resignation of Secretary of State Brad Raffensperger (R), who has denounced the president's claims and stood by the integrity of the vote.

On Friday, Trump tweeted that the Georgia runoffs are “both illegal and invalid” and would not be legitimate because of one of the state’s legal settlements. He said he would still rally for the Republican candidates, with his trip to the state scheduled for Monday in Dalton. He also told Georgians to “get ready to vote on Tuesday.”

But his consistent claims mean that Republican voters continue to hear a contradictory message from their party: Vote in large numbers in a system that the GOP’s most popular politician says is riddled with fraud.

On Saturday, a growing coalition of Republican senators announced plans to block the formal certification of Biden’s victory and called for an emergency 10-day audit to investigate Trump’s unfounded claims. Trump tweeted afterward that there would be “plenty more to come.” Like previous attempts to overturn the election results, the bid will probably fail. But the controversy will command attention at a time when Republicans want GOP Georgians to be hear one unified message: Vote.

Also Saturday, Trump raised the topic of the runoffs in a phone call with Raffensperger, in which he pressed the secretary of state to change the outcome of the presidential race, according to a recording of the conversation obtained by The Washington Post.

"You have a big election coming up and because of what you've done to the president — you know, the people of Georgia know that this was a scam," Trump said. "Because of what you've done to the president, a lot of people aren't going out to vote, and a lot of Republicans are going to vote negative, because they hate what you did to the president."

Democrats on Sunday sought to leverage the Republican infighting.

Harris, appearing with Warnock and Ossoff, referred to Trump’s call with Raffensperger as the “voice of desperation” and a “baldfaced, bold abuse of power by the president of the United States.”

Former Georgia gubernatorial candidate Stacey Abrams (D) called Perdue and Loeffler “feckless hypocrites” in their handling of the issues confronting Republicans.

“They have waffled back and forth on whether they care about the future of Georgia, and they’ve done very little to show any real concern for Georgia lives,” Abrams said on NBC News’s “Meet the Press.”

Democrats and independent groups have aggressively courted Black voters, hoping to form the same coalition that helped Biden win the state in November. They have been bolstered by early-voting numbers that have shown high turnout in areas with more Democrats and have sought to press any advantage by casting Republicans as wrong on economic issues and overly deferential to a president trying to overturn the will of the American people.

“If you send me and Reverend Warnock to the Senate, we’ll deliver the $2,000 stimulus check that people need to stay in their homes, that families need to stay on their feet,” Ossoff said Saturday.

Ossoff and Warnock have used the drama of the past week to paint their Republican counterparts as out-of-touch millionaires who worked to shore up their own pre-pandemic finances while delivering only paltry support to struggling Georgians.

The events of the past week underscored the challenges facing Perdue and Loeffler as they seek to retain their seats.

Both had voted in favor of a stimulus measure that included $600 checks for many Americans. Trump, who had remained mostly on the sidelines while his administration negotiated the legislation, stunned Republicans when he called it a “disgrace” and said the amount that goes to Americans should be increased to $2,000.

Loeffler and Perdue later publicly agreed with Trump — and congressional Democrats — who sought to increase the stimulus checks to that amount.

But McConnell said he saw no path for the legislation to pass, effectively killing the legislation.

Then both senators avoided casting a politically awkward vote late last week when the Senate voted overwhelmingly to override Trump’s veto of a defense authorization bill — but Georgia’s senators weren’t there.

Asked by Baier on Sunday why she didn’t vote to protect Trump’s veto, Loeffler demurred.

“Well, look, I stood with the president 100 percent of the time. He’s putting America first. He’s fought for our men and women in the military. He restored our strength in our Department of Defense and our national security,” she said. “But, look, I have to be out across the state campaigning to make sure that Georgians turn out and vote on January 5, because none of this will matter if we don’t win on the 5th.”

When Loeffler repeatedly declined to say how she would have voted on the veto had she been present, Bair concluded: “That’s not a yes or no.”

“That’s right,” Loeffler replied.

David Weigel and Paulina Firozi contributed to this report.