Though polls show Ms. Abrams and Mr. Kemp in a very tight race, she has some odds to beat, and not just the odds of being a black female Democrat running for statewide office. In 2016, President Trump won 51 percent of the Georgia vote to Hillary Clinton’s 45.9 percent. Mr. Kemp, who has been accused of overseeing voter suppression as secretary of state, is running a Trumpian campaign full of conservative appeals on issues like immigration and tax cuts that animate the president’s base.

In recent weeks, Mr. Kemp has worked to soften his image, but one campaign ad this summer depicts him revving up a chain saw, posing with his firearms collection and showing off his pickup truck.

“I got a big truck,” he drawls, slamming the driver’s side door, “just in case I need to round up criminal illegals and take ’em home myself.”

Both candidates are running hard on job creation and pro-business policies. This summer Ms. Abrams visited every one of Georgia’s 159 counties, many of them in deeply Republican areas, with the same wonkish, detail-obsessed message delivered in the same rapid-fire cadences: Georgia needs more jobs, more public transportation, better infrastructure, better rural health care. It needs gun control. It needs to allow its citizens to vote. It does not need a religious freedom law, championed by Mr. Kemp, that Ms. Abrams says would protect one group while discriminating against others.

This race is also about race. How could it not be, given who she is, where she is from, and the state she hopes to lead? She has declared that the massive pro-Confederate carving at Stone Mountain, just east of Atlanta, should be taken down, just as the Confederate imagery on the old state flag had to go.

But she is much more likely to discuss her desire to expand Medicaid under the Affordable Care Act — a liberal idea, but one she believes will resonate across racial and party lines in a state with an acute rural health care crisis. If Medicaid expansion was embraced by Indiana under then-Gov. Mike Pence, she likes to say, why shouldn’t it be embraced by Georgia?