Sliding in the polls, and under attack even by prominent figures in his own party, the usually self-assured Mr. Trump seemed to break character, lamenting his predicament, and even asking for help, before a group of 700 evangelical pastors and church leaders in Orlando, Fla.

“We’re having a tremendous problem in Utah,” Mr. Trump said, alluding to polls showing him in a fight with Mrs. Clinton in that normally deep-red state. “Utah is different.”

In Ohio, Mr. Trump said, “We need help.”

In Pennsylvania, a state he once insisted he would win, he seemed now to hold out hope of an upset that was looking more like a long-shot. “Pennsylvania is a little further, but I think we’ll win Pennsylvania because of the miners,” he said, adding of Mrs. Clinton: “She wants the miners out of business. She wants steel out of business.”