CUTHBERT, Ga. — As Stacey Abrams began her second campaign for Georgia governor with a speech this week about Medicaid expansion in front of a shuttered rural hospital, the crowd of about 50 peppered her with questions on issues like paving new roads.

But Sandra Willis, the mayor pro tem of this town of roughly 3,500 people, had a broader point to make. “Once you get elected, you won’t forget us, will you?” she asked.

The question reflected Ms. Abrams’s status as a national Democratic celebrity, who was widely credited with helping to deliver Georgia for her party in the 2020 elections and has made her name synonymous with the fight for voting rights.

But she has shown little desire to put ballot access at the center of her bid. Her first days on the campaign trail have been spent largely in small, rural towns like Cuthbert, where she is more interested in discussing Medicaid expansion and aid to small businesses than the flagship issue that helped catapult her to national fame.

Ms. Abrams’s strategy amounts to a major bet that her campaign can survive a bleak election year for Democrats by capitalizing on Georgia’s fast-changing demographics and winning over on-the-fence voters who want their governor to largely stay above the fray of national political battles.

“I am a Georgian first,” she said in an interview. “And my job is to spend especially these first few months anchoring the conversation about Georgia.”

In Cuthbert, where Ms. Abrams was pressed on Monday by Ms. Willis on her commitment to Georgia’s small communities, she reminded onlookers that this was not her first visit to town — and she promised it would not be her last. The town sits in Randolph County, one of a handful of rural, predominantly Black counties that were crucial to Democrats’ victories in Georgia in the last cycle. Upward of 96 percent of Black voters who cast ballots here in the 2020 presidential election voted in the 2021 Senate runoff elections.

Randolph has also been held up as an example of the state’s neglect of its low-income, rural residents: The county’s only hospital shut down in October 2020.

“I’m here to help,” Ms. Abrams said in her Monday speech in front of the closed hospital. Listing the names of seven counties surrounding Randolph, she promised to be a “governor for all of Georgia, especially southwest Georgia.”

Ms. Abrams’s focus on state and hyperlocal issues reflects an understanding that to win Georgia, any Democrat must capture votes in all corners of the state. That also means knowing the issues closest to voters in every corner.

“Everything either happens in Atlanta, or outside of Atlanta in the suburbs,” said Bobby Jenkins, the mayor of Cuthbert and a Democrat. “But as the election in November showed, you’ve got a lot of Democrats, a lot of people in these rural areas, and you cannot overlook them. There aren’t many in this county. But when you band all of these counties together in southwest Georgia, then you can create some impact.”

Ms. Abrams has also used visits like the one to Cuthbert and a later meet-and-greet in the central Georgia town of Warner Robins to criticize Gov. Brian Kemp, a Republican who beat her in the same race in 2018, over what she called his weakening of the state’s public health infrastructure during the pandemic and his underinvestment in rural communities.

“If we do not have a governor who sees and focuses on how Georgia can mitigate these harms, how Georgia can bolster opportunity, then the national environment is less relevant, because the deepest pain comes from closer to home,” Ms. Abrams said in the interview.

Still, that national environment remains unfriendly to Democrats. Less than eight months before the November midterm elections, the party is staring down a record number of House retirements, a failure to pass the bulk of President Biden’s agenda and a pessimistic electorate that is driving his low approval ratings.

Yet Democrats see reasons for hope in Georgia. The state continues to grow younger and more racially diverse, in a boon to the network of organizations that helped turn out the voters who flipped Georgia blue in 2020. Many of those groups remain well-staffed and well-funded. And while Ms. Abrams is running unopposed in the Democratic primary, Mr. Kemp faces four challengers, including a Trump-backed candidate, former Senator David Perdue.

All of this is why, while Ms. Abrams’s public image has expanded, she has not deviated much from the campaign strategy she employed in 2018. During her first run for governor, she visited all 159 of Georgia’s counties and aimed for surges in turnout in deep-blue metro Atlanta counties even as she sought to turn out new voters in rural areas that Democrats had historically ceded to Republicans. Several of her 2022 campaign staff members formed her 2018 brain trust.

Voting rights activists in the state — many of whom say their relationship with Ms. Abrams and her campaign remains warm — hesitate to question Ms. Abrams’s reduced focus on ballot access, especially since it is so early in the campaign and her strategy could yet shift.

“She has a certain star, national spotlight quality that you rarely see with Southern candidates,” said LaTosha Brown, a co-founder of the group Black Voters Matter in Georgia. She expressed confidence that Ms. Abrams’s candidacy would “continue to keep the voting rights issue from dying.”

Ms. Abrams’s organizing for voting rights has its roots in her years as the minority leader in the Georgia Statehouse. She founded the voter enfranchisement group New Georgia Project in 2013 to turn out more young and infrequent voters — a strategy she pitched to national Democrats ahead of the 2020 election amid efforts to persuade white moderate voters.

Then, a year ago, after Georgia’s Republican-led legislature passed a sweeping bill of voting restrictions, ballot access again became a central issue for national Democrats. Amid the party’s uproar about the bill and others like it, Ms. Abrams focused on the policy implications of the legislation over the political. During testimony to Republican senators in Washington shortly after the law’s passage, she laid out a laundry list of criticisms of the measure, denouncing its limits on drop boxes and a reduction in election precincts that could deter working people from voting.

For their part, Republicans are eager to portray Ms. Abrams as an influential national figure — but a dangerous, radical one, whom they will try to beat at all costs.

Her critics on the right have also aimed to paint her as a sore loser, citing her yearslong insistence that Mr. Kemp’s 2018 victory over her owed to voter suppression tactics that he employed as the Georgia secretary of state. Some have even compared her to former President Donald J. Trump in her unwillingness to accept unfavorable election results.

“Stacey Abrams spent the last four years chasing style-magazine covers, championing the national Democrats’ dangerous far-left agenda, and waging shadow campaigns for president and vice president,” said Tate Mitchell, a spokesman for Mr. Kemp. “For her, this campaign for governor is about attaining more money and power — not putting hardworking Georgians first.”

But she has been careful to counter that narrative, making clear in her recent campaign speeches that she did not win in 2018.

“Four years ago, when I applied for this job of governor, I had my application declined,” she told supporters in Atlanta on Monday. “That’s OK. I’ve had four years to work on things. I’ve had four years to live up to what I told folks I would do when I was running for office.”

During her speech in Atlanta, Ms. Abrams mentioned voting rights only briefly, alluding to the state’s new voting law as she warned of a Republican backlash to Democrats’ inroads in Georgia in recent election cycles.

In the interview, she said that in 2018, she had underestimated the extent of limits on access to the ballot.

“I was aware of the general architecture,” Ms. Abrams said. “I was not aware of just how deeply embedded it had become in the conduct of our elections. And that is not something that will surprise me again.”