Stacey Abrams was a high school senior the first time she was invited to the Georgia governor’s mansion. It was for a ceremony honoring the state’s class valedictorians, and Abrams was her school’s top academic achiever. At the time, her family did not own a car, so Abrams and her parents rode the bus from their working-class suburb to the stately mansion in downtown Atlanta.

When they arrived, Abrams recalls a guard emerging from the security booth. Eyeing the bus, he told them: “This is a private event. You don’t belong here.” Never mind that her invitation was tucked into her mother’s handbag or that her name was second on the list of invitees.

A terse exchange ensued between her father and the guard, who grudgingly checked the guest list and let them in.

“The thing of it is,” Abrams said at a recent campaign stop in Atlanta, “I don’t remember meeting the governor of Georgia. I don’t remember meeting my fellow valedictorians from 180 school districts … All I remember is a man standing in front of the most powerful place in Georgia, looking at me, telling me I don’t belong.”

But the story doesn’t have to end there, Abrams tells supporters as she campaigns to become the first Black female governor in American history. With their help this November, she promises, they will “open those gates wide” and “win the future for Georgia”.

Four years ago, Abrams came within a hair of it. She lost the Georgia governorship to Republican Brian Kemp by fewer than 55,000 votes, in a race dominated by allegations of voter suppression, which Kemp, then the secretary of state overseeing the election, denied.

In her near-miss, national Democrats saw a promising leader – and the potential to reclaim the southern state that had long ago slipped away. Successive Democratic wins in the years that followed validated her work expanding the electorate, a decade-long project aimed at mobilizing the disillusioned and the marginalized.

Abrams was even considered a potential running mate for Joe Biden in 2020, a prospect she welcomed. But she always kept her sights on the governor’s mansion, declining pleas to run for the Senate. Now, her second chance has arrived.

Yet Abrams, hailed by Democrats as the architect of Georgia’s political transformation, enters the final weeks of her rematch with Kemp an underdog.

Polls consistently show the 48-year-old Democrat trailing Kemp, now a relatively popular governor with the advantage of incumbency. The latest Atlanta Journal-Constitution (AJC) poll found that the governor had significantly expanded his lead over Abrams, 50% to 42%. And while Abrams has stronger support among her base than Kemp, according to a Monmouth University survey, it concluded that her path to victory was “much narrower”.

But Abrams is refusing to be counted out. A Yale-educated tax attorney, she says she trusts her math better than the polls. In the fast-growing and diversifying battleground state, she notes that as many as 1.6 million new voters have been added to the rolls since 2018, many times Kemp’s margin of victory that year.

“Every success I’ve ever had in politics has been about building the electorate I need – building the electorate we should have, which is an electorate that’s much more reflective of the state,” Abrams said during an interview at a coffee shop in Atlanta.

Georgia is nearly evenly divided between the parties, and in many ways, Abrams and Kemp embody the dueling factions of the state’s polarized electorate. Abrams, a former state house minority leader and prominent voting rights advocate, is working to mobilize Black, Latino and Asian American voters along with young people in Atlanta and its sprawling suburbs. While Kemp, a staunch conservative who easily defeated a Trump-backed primary challenge earlier this year, draws overwhelming support from white voters in the rural and exurban parts of the state.

“This is 100% the battle of the bases,” said Nsé Ufot, leader of the New Georgia Project, a group founded by Abrams to register and engage young people and voters of color. “And it’s 100% going to be determined by who shows up to vote and whose votes get counted.”

Canvassers with the New Georgia Project are pounding the pavement to register and turn out voters this cycle. Their goal is to knock on at least 2m doors by election day.

Though some Democrats have expressed doubts about Abrams’ expansion strategy, Ufot said it has already proven effective by paving the way for Biden’s victory in 2020 and the election of two Democratic senators in 2021, which delivered the party control of the chamber.

“Now is the time to double down, not to second guess ourselves,” she said.

Despite a deeply loyal base, surveys suggest Abrams has become a more polarizing figure since her last campaign. Supporters say it is not surprising, after four years of being vilified by conservatives as a far-left extremist who views the governorship only as a stepping stone to the presidency.

But it may be making it harder for Abrams to attract the vanishingly thin slice of independent and moderate Republican voters whose discomfort with Trump pushed them toward Democrats in recent elections. A Marist Poll found that 11% of Georgians who voted for Biden in 2020 plan to back Kemp for governor, while just 5% of Trump voters favor Abrams.

“If Abrams looks to be more than a contender and she wants to win,” said Andra Gillespie, a political scientist at Emory University in Atlanta, “she really is going to have to shake the tree and find a few more Democratic voters.”

Meanwhile, Trump loyalists who were once wary of Kemp have largely aligned behind him, persuaded by his conservative record and their fear of an Abrams victory.

“We definitely cannot have a Stacey Abrams governorship in Georgia,” said Salleigh Grubbs, chair of the Cobb County Republican party, which censured Kemp in 2021. “That’s a very scary proposition.”

Kemp’s refusal to overturn Biden’s victory in Georgia during the turbulent weeks after the 2020 election infuriated Trump. In the months that followed, he made Kemp the target of a vengeance campaign, even once musing that Abrams would make a better governor.

But since Kemp’s strong primary showing, Trump has mostly stayed away from the governor’s race. And Republican allies say Kemp’s independence will probably help him win back disaffected suburban voters.

Abrams is vocal in her view that Kemp deserves no credit for withstanding pressure to subvert a free and fair election.

“While I’m glad that he didn’t commit treason, that is not a reason to lionize him,” she said in the interview. “He simply did not do one thing and he has used that to cloak every other bad behavior.”

Kemp, Abrams argues, has been relatively silent on Trump’s efforts to overturn the election, even as the former president’s stolen-election myth continues to resonate deeply with conservatives in the state. He also backed an overhaul of the state’s voting laws that critics said was rooted in Trump’s groundless claims of widespread fraud.

“Kemp is a Maga Republican who has done everything in his power to align himself with not only Trump’s values but Trump’s behavior,” she added. “He has just done it in a more subtle way.”

In Georgia, like elsewhere, Democrats face a challenging political environment. Voters have soured on the president amid widespread economic malaise and anxiety about the rising cost of living.

With the economy top of mind for voters, Kemp has sought to tie Abrams to Biden and warned that her economic plans would deepen inflation. At the same time, he is campaigning as a steward of Georgia’s bustling economy, which includes record-low unemployment and a record $21.2bn in state-tracked business investments.

According to the AJC poll, Georgians were significantly more pessimistic about the direction of the country than the direction of their state. On the campaign trail, Kemp attributes the rosier outlook to his decision to reopen businesses after they closed during the earliest months of the pandemic. He also approved of popular policies that boosted teacher pay, provided tax rebates to families and suspended the state’s gas tax.

“The courage that we have seen from Governor Brian Kemp has been extraordinary,” said Nikki Haley, the former Republican governor of South Carolina, during a campaign appearance with Kemp at a burger joint in Atlanta. “First state in the country to open up after Covid – he was vilified for it, and it turns out that he’s the one that saved the economy, saved our businesses … and allowed people to get back to work.”

Abrams has sought to paint a starkly different picture of the economy under Kemp, one in which the wealthiest have profited while the poor have been left behind. At the center of her economic agenda is a plan to fully expand Medicaid, which she argues is critical to stopping a wave of hospital closures across the state, including a major trauma center in Atlanta that has become a flashpoint in the campaign.

But it is a brewing national backlash to the supreme court decision overturning the federal right to an abortion that Abrams and Democrats believe could change the tide. In ads and on the campaign trail, Abrams has lashed Kemp for signing a 2019 law that bans abortion as early as six weeks in Georgia, before many women know they are pregnant. The law was allowed to take effect in the aftermath of the high court’s ruling.

According to recent polling, most voters in Georgia disagree with the supreme court decision in Dobbs v Jackson Women’s Health Organization and more than half say the state’s abortion laws are too strict.

“The No 1 issue that people talk about when I’m on the campaign trail is abortion rights,” said Nabilah Islam, the Democratic nominee for a competitive state senate seat in Gwinnett county.

Islam, who has put abortion access at the center of her campaign, pointed to the rise in voter registration among women since the Dobbs decision. “There’s a feeling of helplessness,” she said, “but also hope because people are so angry that they’re organizing at levels unseen before.”

Abrams is also working to shore up her base. Black voters are the cornerstone of the Democrats coalition in Georgia. While they still overwhelmingly prefer Democrats, there are some signs the party is struggling to motivate Black voters at the levels needed to win in Georgia.

The trend is particularly pronounced among Black men, who have edged toward Republicans in recent years. In several polls, Kemp has notably improved his standing among Black voters from 2018.

Abrams says she is taking no vote for granted. As part of her campaign’s outreach to Black men, she has hosted a series of conversations called “Stacey and the Fellas” to discuss how her initiatives on issues like healthcare and housing will benefit their communities.

At one such event over the summer, she was blunt: “If Black men vote for me, I will win Georgia.”

Andrekay Askew is among the roughly one in 10 Black voters who remain undecided in the state. The 27-year-old said he is skeptical of Democrats’ economic policies but was open to learning more about Abrams’s platform.

Ultimately, he said, his decision would be guided by: “Who is better with the money?”

Listening from the porch, his mother shook her head in disagreement. Laqua Askew, who works in special education, is a lifelong Democrat who voted for Abrams in 2018 and plans to do so again this year. She is worried about a lack of public school funding, as well as gun violence and crime, all of which she said takes a heavy toll on the low-income students she works with.

“Kemp had the opportunity to make a change but he hasn’t,” she said. “We’ve got to try something else.”

In a state as closely divided as Georgia, much could still change before election day. Kemp and Abrams will face off in a public debate that could help sway the critical few undecided voters. And if neither candidate wins a majority of the vote, the contest proceeds to a runoff election.

Speaking at the AFL-CIO Labor Day picnic last month, Abrams asked supporters to spend the final weeks of the campaign focused on the “unfinished business” before them.

“I can’t get this job if you all don’t show up,” she said. “I can get this job if you all do what you did in 2018.”

• Joan E Greve contributed to this report from Atlanta.