They were also out of character given her usual studied care in choosing words. Her campaign slogan is “Stronger Together,” and she has built her message around inclusiveness, in contrast to denigrating comments Mr. Trump has made about Mexicans, Muslims, women and other groups. Much of her ad campaign is built around using Mr. Trump’s comments to portray him as an unsuitable leader.

But for all the policies she says would lift middle-class wages and alleviate income inequality, Mrs. Clinton has struggled with the perception by many voters that she is not on their side. Asked whether they thought Mrs. Clinton understands the needs and problems of people like themselves, 53 percent of registered voters said she did not, according to a CBS News poll from June.

The Democratic National Convention in July and a bus tour in Pennsylvania and Ohio laser-focused on kitchen-table issues seemed to help Mrs. Clinton. In an August ABC News/Washington Post poll, 55 percent of Americans said Mrs. Clinton understood the problems of people like them better than Mr. Trump, compared with 35 percent who named him.

But Mrs. Clinton devoted much of August to fund-raising in the moneyed enclaves of the Hamptons and Martha’s Vineyard. At some of these events, which were closed to the press, she uses the “baskets” characterization of Trump voters.

After barring the press from most fund-raisers, the Clinton campaign has tried to be more open in the post-Labor Day sprint. Aides allowed a small group of reporters in Mrs. Clinton’s regular press corps to cover the Friday event, which took place at Cipriani on Wall Street and for a contribution of $1,200 to $10,000 included performances by Barbra Streisand and Rufus Wainwright.

A spokesman for the Trump campaign, Jason Miller, said what made Mrs. Clinton’s comments particularly off-putting was that she made them “in front of wealthy donors” and that the setting and statement, “revealed just how little she thinks of the hard-working men and women of America.”