Republicans’ 2022 Lesson: Voters Who Trust Elections Are More Likely to Vote

His campaign sent canvassers to voters’ doors, asking if they had requested or sent in their mail ballots. He held events at early voting locations, encouraging everyone to cast a ballot early if possible. (It’s a tradition he carried into the governor’s office, and he voted early in November, too.)

“I think when the autopsies are written about 2022, the early vote and the absentee vote are going to be a huge part of it and something that our party really needs to embrace early on,” said Kristin Davison, a political adviser to Mr. Youngkin.

In Arizona, Republicans calculated that a series of Trump-style rallies, and excitement around Ms. Lake among the conservative faithful, would lead to an overwhelming show of force on Election Day that would surpass the Democrats’ mail votes.

Where Ms. Lake was trying to move her voters en masse in one big Election Day push, the campaign of her opponent, Ms. Hobbs, relied heavily on mail voting and was quietly working to send supporters to the polls in a targeted fashion.

“Every few days or so we get the list of voters who turned in their ballot, we can remove them from our universe, so we are only talking to voters who haven’t voted yet,” said Nicole DeMont, Ms. Hobbs’s campaign manager. “If they were telling everybody to vote on Election Day, you’re never shrinking your universe.”

Local Republicans appeared to have second thoughts as the campaign entered its final week, when the chair of the state party, Kelli Ward, a loud proponent of the stolen-election narrative, posted a photo of herself on Twitter placing her ballot in a drop box.

Yet Ms. Lake’s campaign remained vulnerable to the myriad forces that can come to bear on that single day — when a sick child or the weather or the demands of work may keep people from going to polls or, in the event of lines, keep them from staying long enough vote.