“This is strictly a business decision,” a Carrier executive tells employees, describing how their 1,400 jobs making furnaces and heating equipment will be sent to Mexico. Workers there typically earn about $19 a day — less than what many on the assembly line here make in an hour. As boos and curses erupt from the crowd, the executive says, “Please quiet down.”

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At the same time, a chronic trade deficit and an overvalued dollar have caused factory jobs to dry up, contributing to a deep divide between the political and economic elite and the rest of the nation. Perhaps a clash was inevitable. Consider the case of Ms. Shanklin-Hawkins. While she says she won’t be voting for Mr. Trump and considers him a racist, she applauds his message on trade. She says she plans to vote for Senator Bernie Sanders of Vermont, who similarly blasts free trade, but from the left. The two populist candidates may be political opposites, but when it comes to the downside of globalization, Mr. Sanders and Mr. Trump are speaking to her with one voice.

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But Akhil Johri, the chief financial officer, noted that recent factory consolidation was among the reasons Carrier’s management is eyeing a list of targets for future cuts. “They are painful” but are necessary “for the long-term, competitive nature of the business and shareholder value creation,” he said. “We feel good about being able to execute on that.”

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Wall Street is looking for United Technologies to post a 17 percent increase in earnings per share over the next two years, even though sales are expected to rise only 8 percent. Bridging that gap means cutting costs wherever savings can be found, as Mr. McDonough suggested at the meeting with analysts.

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Over all, United Technologies earned nearly $7.6 billion last year, and $2.9 billion of that came from the climate, controls and security division that includes Carrier. Those profits aren’t under pressure; in fact, margins in the unit have steadily expanded in recent years.