A marathon election campaign will enter its final sprint on Tuesday when voters in Georgia decide the last seat in the US Senate – and shape the next phase of Joe Biden’s presidency.

Opinion polls suggest a narrow lead for incumbent Democratic senator Raphael Warnock over his Republican challenger, former American football star Herschel Walker.

Victory for Warnock would give Democrats 51 seats in the 100-seat Senate, a stronger hand than they currently hold in an evenly split chamber where Vice-President Kamala Harris casts the tiebreaker.

It is the second time in two years that a Senate race has gone to a runoff in Georgia because neither candidate secured a majority on election day. But the Peach State is showing little sign of election fatigue with officials reporting record early voting turnout.

National and state Democrats are also not slowing down as they come out to support Warnock. Last week saw celebrity-led events including a concert by the Dave Matthews Band, canvassing with actresses Tessa Thompson and America Ferrera, and a rally targeting Georgia’s Asian American community featuring Jeannie Mai Jenkins and Daniel Dae Kim.

Warnock, pastor of Martin Luther King’s former church, closed out the week with a rally in Atlanta led by the party’s biggest star, Barack Obama. “I’m here to tell you that we can’t let up,” the ex-president said after ascending the stage to roars and chants. “I’m here to tell you we can’t tune out. We can’t be complacent. We have to run through the tape. And I know you can do it because you did it before.”

The event felt like a baptist sermon as, with nearly every sentence the former president uttered, the crowd cheered and responded with “yeah,” “alright,” and “come-on,” illustrating Georgia’s geography in the deep south squarely in the Bible Belt.

Obama has been liberated, punchy and sardonic on the midterm campaign trail, eviscerating Republicans in a way that few Democrats can. He said: “Since the last time I was here, Mr Walker has been talking about issues that are of great importance to the people of Georgia. Like whether it’s better to be a vampire or a werewolf. This is a debate that I must confess I once had myself. When I was seven. Then I grew up.”

He added: “In case you’re wondering, by the way, Mr Walker decided he wanted to be a werewolf. Which is great. As far as I’m concerned, he can be anything he wants to be, except for a United States senator.”

As Florida turns Republican red, Georgia is emerging as one of the most critical swing states in the country. Biden’s victory over President Donald Trump there in 2020 helped propel him to the White House. Warnock and fellow Democrat Jon Ossoff won Senate seats in January 2021 following a runoff, giving their party control of the chamber.

Obama praised Georgians’ ability to influence the landscape of national politics, reeling off post-2020 achievements such as infrastructure spending, gun safety legislation, cuts to prescription drug prices and a record investment in clean energy. “That happened because of you, Georgia. And now we need you to do it again.”

Democrats hope that Obama’s intervention will energise the party base. Ashley Davis, a student who attended the rally, said: “I’m ready. I’ve been canvassing since the start of the election, and I am phone banking too. I am feeling invigorated by that speech because it’s so true. We can’t stop because we know what’s at stake. Georgia is ready, and we have shown that we are a force to be reckoned with.”

Biden, by contrast, has stayed away amid concerns that he could be a drag on Warnock. Instead he is aiming to help the campaign from afar, a strategy that proved successful in the midterms as Democrats defied expectations.

On Friday the president joined a phone bank run by the International Brotherhood of Electrical Workers in Boston, Massachusetts, to help Warnock’s campaign and drew a sharp contrast with Walker. “This is not a referendum on Warnock,” he said. “This is a choice – a choice between two men … One doesn’t deserve to be in the United States Senate based on his veracity and what he said and what he hadn’t said. The other man is a really, truly decent, honourable guy.”

Republicans won every other statewide Georgia race last month. Governor Brian Kemp, who won re-election, has now thrown his weight behind Walker. A strong election day turnout by the party’s voters could still push the ex-football player to victory.

But Walker has proved a motivator for Democratic enthusiasm because he is endorsed by Trump, lacks political pedigree and has made a series of weird and wild statements. One flyer mailed to homes by the Democratic Party of Georgia asks: “How embarrassed would you be if Herschel Walker was your senator?”

Walker’s campaign has been plagued by accusations that he abused girlfriends in the past and paid for their abortions, undermining his anti-abortion stance. Recently he has faced claims that he maintains his primary residence in Texas, not Georgia. Walker has denied the allegations.

Warnock narrowly edged Walker in the 8 November election by 49.44% to 48.49%. An Emerson College Polling/ The Hill survey of Georgia voters found Warnock at 49% support and Walker at 47%, with 4% undecided.

John Zogby, an author and pollster, said: “Warnock must have gotten some kind of momentum from November 8 because Black voters appear to be more energised and they’re not going with Herschel Walker.

“Walker’s had a number of issues that he’s had to contend with since November 8 and and he hasn’t handled them well. Even with Kemp’s help, which could be considerable, ultimately voters are not voting for who the governor wants them to vote for: they’re voting for the candidate.”

While Democrats have already guaranteed control of the Senate for another two years, a true majority of 51 seats would speed up the confirmation process for Biden’s administrative and judicial nominees and provide a cushion for the president should any Democrats buck the party line.

In addition, Democrats would gain more seats and financial resources on Senate committees, and committee chairs would no longer need any Republican support to issue subpoenas compelling witness testimony during investigations.

Biden told reporters last month: “It’s always better with 51, because we’re in a situation where you don’t have to have an even makeup of the committees. And so that’s why it’s important, mostly. But it’s just simply better. The bigger the numbers, the better.”

Larry Sabato, director of the Center for Politics at the University of Virginia, said: “It does make a big difference because Democrats would get a majority on almost all the committees. Court appointments will go zip, zip, zip because you get access to the floor much more easily as a clear majority party in the Senate.

“Also, look how many old senators there are … If there’s an open seat and people are upset at Biden, they could end up voting Republican in any purple state.”