But marshaling that residual anger to unseat an incumbent is not an easy feat. Mr. Raffensperger has worked to win back Republicans by casting himself as a defender of “election integrity,” even as he has spent hours debunking a laundry list of false claims about the 2020 election. Some voters’ memories and passions have faded. Many never had strong opinions about their secretary of state.

It all has made the race one of the purest tests yet of whether the 2020 election lie can be weaponized to win elections. While polls have shown that leagues of Republican voters in Georgia and elsewhere largely embraced the fiction that the 2020 election was “stolen” in its immediate aftermath, it is not clear those concerns alone, or Mr. Trump’s personal vendetta, are enough to drive voters’ choices…

Most of the young Republicans in the room said they wanted to hear what Mr. Hice would do differently from Mr. Raffensperger in elections should he be elected.

“Even if you’re not a dogmatic, election-was-stolen person, there are a lot of people with reasonable doubt, and that reasonable suspicion is fair,” said Chris Campbell, 39, a national accounts manager at SmartFeeds. “Raffensperger didn’t address those concerns well, and people don’t have confidence in him. But I do have confidence in Hice and trust that he would run the office with integrity.”