Democrats, prompted by Mr. Trump’s latest antics and the string of Republicans who have spoken out against him, have, perhaps prematurely, started discussing a loftier goal than just winning in November: a wide margin of victory, driven by a record turnout among black, Latino and young voters, that could help squash Mr. Trump’s movement.

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David Plouffe, President Obama’s former campaign manager, proposed the idea in June. “It is not enough to simply beat Trump,” he wrote on Twitter. “He must be destroyed thoroughly. His kind must not rise again.”

The proposition seemed far-fetched at the time, given the realities of the electoral map and Mrs. Clinton’s weaknesses. But in recent days, Democrats and advisers have, delicately, embraced the idea.

“The first order of business is winning,” said Geoff Garin, a strategist for Mrs. Clinton’s 2008 campaign who now advises Priorities USA Action, a pro-Clinton “super PAC.” “But the larger stakes of the election are putting the country on a path where Trump’s views of the world are far in our rearview mirror.”