"If there’s anything the last four years have taught us, it’s that elections have profound consequences and those who want to retain our democracy and make racial, social, and economic progress in this country have to think strategically about the fights we wage," the groups write in a letter to Lieberman, published Friday. "We urge you, with everything we have, to do the right thing for our country, (and) end your race for U.S. Senate."
The groups signing onto the letter include Democracy for America, who's CEO is ABC News contributor Yvette Simpson, and Justice Democrats, a group co-founded by "The Young Turks" founder and host Cenk Uygur in January 2017, which boasts Rep. Alexandria Ocasio-Cortez as one of its candidate success stories.
Eight other groups are signatories to the letter, and together represent "tens of thousands of grassroots activists in Georgia and millions across the country." They write that they wouldn't normally push for a Democrat to exit the race during a primary, but the stakes of this election are too high.
Unlike a regular Senate race, every candidate, regardless of party affiliation, will compete on the same ballot in November. In Georgia, to win outright, a candidate has to amass a majority of the vote; otherwise, the top two vote-getters advance to a runoff election.
There are 21 candidates on the ballot, and voting is already underway in Georgia. More than 132,000 absentee ballots have already been cast, according to data from the secretary of state's office.
One Republican already ended his campaign this week, but it is too late for any candidate to officially drop out and have their name removed from the ballot. Republicans Sen. Kelly Loeffler, the appointed incumbent, and Rep. Doug Collins, have been dueling for GOP support in the battleground state.
These organizations are not the first to call for Lieberman, an entrepreneur and the son of former senator and vice presidential candidate Joe Lieberman, to cease campaigning and work to consolidate support around Warnock, the senior pastor at Ebenezer Baptist Church in Atlanta, where Martin Luther King Jr. served as co-pastor until his death.
But so far, Lieberman has defiantly resisted those calls.
"I'm running for US Senate AS a fed-up citizen of Georgia, and FOR the fed-up citizens of Georgia. The challenges we face are huge. What Georgians of all races want is not a Black senator or a White senator etc, but a GREAT senator," he tweeted on Sept. 24. "That's what I hope to be for ALL of us. That's why I’m staying in the race."
Lieberman has suggested that Warnock would be "beholden" to the Democratic establishment in Washington if elected. He's been endorsed by at least 32 U.S. senators, as well as Georgia native and former President Jimmy Carter and former President Barack Obama, who does not usually endorse when more than one Democrat is on the ballot.
Given the number of candidates competing, this race is expected to advance to a runoff on Jan. 5, as it's highly unlikely anyone can garner more than half the vote.
But the progressive groups' letter expresses hope that if Lieberman ended his campaign, Warnock could do gain enough support to do that.
Since it's a special election, an outright winner could be seated before the new Congress takes the oath of office in January, which the group says could be crucial towards the coming vote on President Donald Trump's Supreme Court pick, Judge Amy Coney Barrett.
A date for the vote before the Senate has not been set yet. The president has called for it to happen before the election, but Senate Majority Leader Mitch McConnell has only committed to it occurring "in the weeks ahead."
"You have a unique opportunity to have a decisive impact on Democrats’ chances in a U.S. Senate race that could stop Senate Republicans from using an illegitimate process to hijack our democracy and force a right-wing extremist onto the Supreme Court for the rest of her life," the groups write in the letter.
In Georgia, election results must be certified by 5 p.m. the 17th day after an election, which would be Nov. 20 this cycle. Even if the vote on Barrett's nomination does not happen until after the general election, and even if Warnock was able to avoid a runoff, it's unclear whether the vote would be delayed that long after the election that he could have a say in it, given the speed with which the president and Republicans are currently moving.
Just a week ago, it looked like Democrats could be in danger of being shut out of the runoff altogether.
A poll from Monmouth University published Sept. 23 showed Loeffler with 23% support among registered voters statewide, Collins with 22% support and Warnock with 21% support. While Warnock had gained significantly -- jumping 13 points since July -- Lieberman had only suffered a 3-point loss, still holding onto 11% in the mid-September poll.
But an even more recent Quinnipiac University poll, published on Tuesday, showed Warnock breaking out from, and even leading, the pack.
Among Georgia likely voters, 31% were supporting Warnock, while 23% were supporting Loeffler, 22% were supporting Collins and 9% were supporting Lieberman.
The Democratic Party of Georgia does not endorse in races with more than one Democrat, but is confident in the party's chances to win this race.
"While Republicans are engaged in their toxic and expensive intraparty fight and also in court to take away health care protections for 1.8 million Georgians with pre-existing conditions, we’re confident that Democrats are in a strong position to flip this seat," Alex Floyd, senior communications adviser, said in a statement to ABC News.