Democratic leaders argue that all of their efforts are consistent with the twin goals of civil rights and economic rights, while they work to hold Mr. Trump accountable for saying that there were “some very fine people on both sides” of the unrest in Virginia.

Ms. O’Connell said that the Democratic Party must stand against the Confederate statues and focus on the problems that face voters daily, like health care and jobs.

The Rise and Organize campaign has rallied Democrats to knock on doors and call people to encourage them to participate in electoral politics.

“People are still asking us about health care. They’re asking us about the economy and about how to raise wages,” Ms. O’Connell said. “And those are the things that we are working on as well.”

But so vague is the slogan #RiseAndOrganize that supporters of Robert James Ritchie, better known as Kid Rock, are using it on Twitter to rally conservatives around the Michigan Republican’s possible Senate campaign. On the left, activists have used it for anti-racism programs, for trying to stop the Dakota Access pipeline and for voter registration.

Republicans say all of this only underscores the president’s contention that Democrats have become the party of obstructionism, blocking progress on overhauling the tax code, on building a wall on the southern border and on reviving the nation’s infrastructure.

In his opinion article, Mr. Schumer called for a concentrated focus on Mr. Trump’s Presidential Advisory Commission on Election Integrity, headed by Vice President Mike Pence and Kansas’ hard-line conservative secretary of state, Kris Kobach.