Should Mr. Trump falter badly in his second debate with Hillary Clinton on Sunday in St. Louis, Republican congressional candidates may take it as a cue to flee openly from their nominee, said two senior Republicans involved at high levels of the campaign who spoke on the condition of anonymity because they were not authorized to discuss private party strategy.

Mr. Trump has already slipped perceptibly in public polls, trailing widely this week in Pennsylvania and by smaller margins in Florida and North Carolina — three states he cannot afford to lose. But private polling by both parties shows an even more precipitous drop, especially among independent voters, moderate Republicans and women, according to a dozen strategists from both parties who spoke on the condition of anonymity because the data was confidential.

Liesl Hickey, a Republican strategist involved in several House races in swing states, said she was dismayed by a sudden exodus of independent voters in more diverse parts of the country.

“They are really starting to pull away from Trump,” said Ms. Hickey, describing his soaring unpopularity with independents as entering “uncharted territory.”