“The politics, substance and morality coincide to make it a winner issue for us in 2016,” Senator Schumer said. “It appeals not just to the people who would benefit,” he added. “Polling data shows it appeals to middle-class people, people of high income.”

The speed with which Democrats and activists have strengthened their demands for minimum-wage hikes poses some complications for both the White House, which has yet to take a position on the Murray plan, and for Hillary Rodham Clinton, who in response to last week’s national protests by low-wage workers wrote on Twitter: “Fast food & child care workers shouldn’t have to march in streets for living wages.”

Mrs. Clinton has a long record of supporting minimum-wage increases, but her recently begun presidential campaign has preferred to ease into revealing the details of her policy positions, the minimum wage included.