Representative Marjorie Taylor Greene of Georgia has supported exhaustive audits of the 2020 results to look for evidence of voting irregularities that repeated reviews have failed to produce. Still, she has told colleagues that she was surprised by a recent survey of Republican voters in her district, according to one person who spoke with her about it.

The internal survey found that 5 percent of Republican voters said they would sit out the 2022 election if the state of Georgia did not conduct a forensic audit of the 2020 election — a demand that some of Mr. Trump’s hard-core supporters have made. Another 4 percent said they would consider sitting out the election absent an audit.

The possibility that nearly 10 percent of Republicans could sit out any election — even one in a solidly red district like the one held by Ms. Taylor Greene — was something Republican strategists said they found alarming.