But even as Democratic candidates universally denounced Mr. Trump’s comments, they did not agree on how the eventual presidential nominee should combat the racial division embedded in those words. Do you, on the campaign trail, talk directly about the president’s inflammatory language, racism and discrimination in this country? Or do you talk about jobs and the economy?

Democratic Party leaders, particularly establishment figures with ties to Barack Obama’s and Hillary Clinton’s presidential campaigns, have largely followed a strategy of careful avoidance: responding to the president’s most inflammatory moments, while attempting to redirect the political debate to what is often described as “kitchen table” issues, such as health care and wages.

However, an increasingly vocal group of Democratic grass-roots organizers and pollsters believe that Mr. Trump’s words and legislative actions amount to a cohesive playbook of white identity politics, meant to court white voters of all economic tiers around the idea that their fates are linked, and are under threat by an increasingly diversifying America. They argue that racism and the public performance of it is a “kitchen table” issue for many voters — black and white — that must be dealt with head-on.

“Just as much time and resources as the nominee spends on targeting and messaging around health care and wages and climate change, they should spend an equal amount of resources around an alternative racial vision for the country,” said Cornell Belcher, a prominent pollster who worked with Mr. Obama. “This isn’t a goddamn distraction.”

Ana Maria Archila, the co-executive director of the progressive group Center for Popular Democracy, said Democrats must embrace this moment as an opportunity.

“You have to be able to speak powerfully about our willingness to belong together,” Ms. Archila said. “Don’t just condemn the racism and the language but use it as an opportunity to argue for a vision of the country in which we can all be included.”