Campaigning recently at a recreation center in Murray County — a rural, mainly white bastion of Republicanism on the Tennessee border — she stood before TV news cameras, reminding people of her work helping to pass a bipartisan billion-dollar transportation bill, and her support of legislation that supports grandparents and other family members raising children.

“I know how to work across the aisle when we need to,” she said.

Ms. Abrams, 44, who favors the expansion of Medicaid under Obamacare and the extension of state scholarships to the immigrants known as Dreamers, has given Republicans many opportunities to argue that she is too far left for a state like Georgia. Senator David Perdue recently called her “the most radical liberal.”

Supporters like Gerald Griggs, a vice president of the state N.A.A.C.P. chapter, reject such descriptions as inaccurate — and also hear in them a coded effort to scare off white voters.

“Definitely, it’s a dog whistle embedded,” he said.

[Democrats see opportunity for gains at the state level.]

Ms. Abrams was elected to the General Assembly in 2006, two years after Republicans had taken control of the Georgia House for the first time in more than a century. She was young, but not green. She had served as student president at Spelman College, Atlanta’s storied African-American women’s college, and kept her life ambitions, eventually including the goal of becoming president, listed in a spreadsheet. “The sheer boldness of my ambitions gnawed at me,” she recalled in her 2018 autobiography, “Minority Leader: How to Lead from the Outside and Make Real Change.”

Style-wise, she was more of a listener than a glad-hander, more policy wonk than enforcer. She was a careful, prepared speaker with a bookish quality, a wry sense of humor and a tendency toward efficiency.

“She engendered a sense of loyalty in a lot of people that way,” said Brian Thomas, who was a member of the House Democratic leadership at the time. “A lot of people just respected the fact that she was just a lot smarter than some of us, and able to use that intellect in ways that were really effective.”