For the Halls, the scrutiny has felt personal. Mr. Hall said that during the debate, Ms. Hall turned to him and jokingly said she might go buy something for herself instead of contributing to another political campaign.

Mr. Hall, 69, made much of his fortune in the real estate industry and said he started a business at 18 with $4,000 from his savings account. Ms. Hall, a lawyer and businesswoman, served as the United States ambassador to Austria under President Bill Clinton after donating to his re-election campaign. Her family has worked in the wine industry since the 1970s.

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As chairman of the Hall Group, which is based in Dallas, Mr. Hall oversees a financial services company, wineries, art exhibits and a luxury hotel. He said that in Texas, he is often seen as the most liberal among friends and business colleagues, part of why he felt unfairly targeted during the debate.

“These people don’t know who they’re talking about when they throw me in the class that they did,” Mr. Hall said of the presidential candidates. “As much as it’s frustrating, it’s more disappointing to me that Democrats are fighting with each other when we have a common goal, which is to get back to the White House.”

On the debate stage, Mr. Buttigieg responded to the attacks by arguing that the views of donors would not influence his positions and saying that his net worth was one-hundredth that of Ms. Warren’s.

Mr. Buttigieg said accepting the contributions of all donors was necessary to “build a campaign ready for the fight of our lives,” referring to the general election face-off against President Trump.

Ms. Warren’s comments also did not sit well with some local residents, who are accustomed to encountering politicians and their high-end contributors. Ms. Pelosi and Gov. Gavin Newsom of California each own a valuable vineyard nearby.