Both Georgia Senate races appear headed for runoffs as Senate control hangs in the balance.

With control of the Senate hanging in the balance, Republicans and Democrats began positioning themselves on Friday for a pair of high-stakes January Senate runoffs in Georgia that could serve as a referendum to cement or upend the results of Tuesday’s election, even as one of the races remained uncalled.

Senator David Perdue, a Republican, was narrowly leading his Democratic opponent, Jon Ossoff, in the uncalled race. But as protracted counting dragged on, he fell below the 50 percent threshold needed to win outright. He was not expected to clear that bar with many of the remaining votes coming from Democratic counties.

Georgia’s special Senate election has been destined for a runoff since Tuesday, when the Rev. Dr. Raphael Warnock, a Democrat, and Senator Kelly Loeffler, a Republican, emerged as the top two vote-getters in a crowded field vying to replace the retired Senator Johnny Isakson.

Democrats would need to win both seats on Jan. 5 — a steep task in a state with deep conservative roots — to draw the Senate to a 50-50 tie, but they were riding a wave of liberal enthusiasm and demographic change that appeared poised to deliver victory in Georgia to a Democratic presidential candidate for the first time since 1992.

If Joseph R. Biden Jr. prevails in winning the White House, his vice president could cast tiebreaking votes to give the party de facto control.

Facing such extraordinarily high stakes, both parties were quickly preparing themselves for a nine-week year-end sprint that some estimated could ultimately cost at least another $100 million and put Georgia at the center of the nation’s political fray just two weeks before Inauguration Day.

Democrats around the country were already mobilizing to use the contests to complete Mr. Biden’s victory and make possible the liberal agenda on health care, the economy and the environment he ran on.

“Change has come to Georgia,” Mr. Ossoff said in a rally in Atlanta on Friday. “And Georgia is a part of the change coming to America.”

Mr. Perdue’s campaign shot back.

“We are excited for overtime — it gives us even more time to continue exposing Jon Ossoff and his radical socialist agenda,” Ben Fry, Mr. Perdue’s campaign manager, said in a statement. “Jon Ossoff does two things well: burn through out-of-state liberal money and lose elections.”

Republicans were ready to try to harness the grievance among Mr. Trump’s most ardent supporters, hoping that the president’s baseless claims of fraud and a backlash to his potential loss could power them to a win in January. Over the last 24 hours, Ms. Loeffler has repeatedly tweeted support for the president, who is falsely claiming that the election is being illegally stolen from him.

Ms. Loeffler said that she had donated to a fund fighting for the president’s cause.

“Praying for four more years of @realDonaldTrump!” she wrote in another message.

With Mr. Trump defying the election results, it was hard to predict how involved he might be in the Senate races. But early Friday morning, he insinuated in a tweet that Democrats were still trying to claim power through nefarious means so they could reverse Republican policies.