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WILLIAMSON, W.Va. — Hillary Clinton came to campaign in coal country — and she had her feet held to the fire.

As Mrs. Clinton stepped onto the sidewalk on Monday to tour a health and wellness center here, a crowd of protesters stood in the rain, many of them holding signs supporting the leading Republican candidate, Donald J. Trump, and chanted, “Go home!”

Later, when Mrs. Clinton sat down with residents to discuss health care and other issues affecting the community and coal miners in particular, the chants of the protesters outside could still be heard.

“No matter what they might be saying out there, they have a friend,” Senator Joe Manchin III, who accompanied Mrs. Clinton, told the panel participants.

But not everyone was buying it.

“Supporting her hurts you,” Bo Copley, a 39-year-old father who tearfully explained that he had lost his job in the coal industry and who struggled to support his family, pointedly told Mr. Manchin.

Mr. Copley then raised a topic with Mrs. Clinton that appeared to be on many of the protesters’ minds (and signs): a remark she made to CNN in March, “We’re going to put a lot of coal miners and coal companies out of business.” How could she say that and now say she wanted to help West Virginians? he asked.

Republicans seized on the remarks — which Mrs. Clinton made in the context of creating clean-energy jobs in areas of the country that had previously depended on coal — and blasted them out as evidence that a Hillary Clinton presidency would hurt coal country. America Rising, an anti-Clinton “super PAC,” called the comments a “brazen disregard for the men and women who help power America.”

Mrs. Clinton told Mr. Copley, whose wife, Lauren, sat next to him at the round table, that her statement in the CNN town hall-style forum “was totally taken out of context” and explained that she had presented a plan to help coal country last summer and was committed to the issue.

“The way things are going now we will continue to lose jobs,” she said. “I didn’t mean that we were going to do it,” but rather “that was going to happen if we don’t take action.”

But, Mrs. Clinton added, “I don’t mind anybody being upset or angry,” given the desperation in Appalachia, where she will spend Monday and Tuesday with campaign events in West Virginia, Kentucky and Ohio. She said, however, that she was “a bit sad and sorry that I gave people an excuse to be angry at me because that’s not what I said at all.”

At one point, Mr. Manchin, who Mrs. Clinton called to apologize after making the remark to CNN, stepped in on the former secretary of state’s behalf. “If I thought she wanted to eliminate one job in West Virginia, I wouldn’t be sitting here,” he told his constituents.

Mrs. Clinton acknowledged she would have a difficult path to win voters over in the May 10 Democratic primary and in the general election.

“I understand the anger and I understand the fear and I understand the disappointment that is being expressed. How could it not be given what’s going on here?” she said. “Because of the misstatement that I made, which I apologized for when I saw how it was being used,” she continued, “I know that my chances are pretty difficult, to be honest.”

As for Mr. Copley, he said he won’t be voting in the Democratic primary. “I’m a registered Republican,” he said.