Facing one of the toughest stretches of his presidential campaign, Donald J. Trump on Thursday acknowledged in unusually candid terms that he faced daunting hurdles in crucial states, as he swung wildly at Hillary Clinton to try to blunt her questions about his fitness to serve in the Oval Office.

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.”