In Congress, where Democrats will take control of the House in January after sweeping victories in the midterms, party leaders have vowed to give electoral overhaul measures a top priority. Bills are planned to make voter registration automatic across the country and to revive provisions of the Voting Rights Act of 1965 that were gutted by the Supreme Court in 2013.

Democrats also thwarted a bid for governor by Kris Kobach, the Kansas secretary of state known for pushing restrictive voting policies that were often struck down in court.

But it was the Georgia governor’s race this year that most angered, and galvanized, the American left, which has portrayed Mr. Kemp, a businessman and ally of President Trump from Athens, Ga., as a vote-suppressing villain.

Mr. Kemp, 55, points to the introduction of an online voter registration system and the substantial growth in the number of registered voters on his watch as evidence that he has made it easier, not harder, for the state’s citizens to register and vote.

Those arguments have done little to stem liberal outrage. The outspoken actor Alec Baldwin recently urged people on Twitter to consider Mr. Kemp’s election “illegitimate,” and the musician Chance the Rapper encouraged his Twitter followers on Tuesday to get behind the Democratic candidate in the runoff for secretary of state, John Barrow.

Ms. Abrams, who emerged from the election as a liberal star, has also begun putting that star power to work for Mr. Barrow, though they come from opposite points of the party compass: She is 44, black, and unabashedly liberal; he is 63, white, and studiously centrist.

In TV ads, Mr. Barrow leans on a fence in front of a bucolic Georgia landscape and declares, “Yeah, I’m a Democrat, but I won’t bite you.”