The grass-roots energy building around the minimum wage issue may upend Hillary Rodham Clinton’s plans to ease into proposing specific economic policies.

The issue will be in the foreground on Wednesday, when fast-food and other low-wage workers plan a nationwide walkout that is expected to draw tens of thousands of people to rally support for a $15-an-hour minimum wage. The protest is the latest show of strength by the Fight for $15, a campaign that economists partly credit with the recent decisions by employers like Walmart and McDonald’s to raise the minimum wage they pay workers.

The daylong strike may provide the first test for the campaign at managing the desire of voters and party activists for an aggressive approach to mitigating income inequality. Mrs. Clinton said that she was running for president because “the deck is still stacked in favor of those at the top,” but she has offered few details about how to bridge that gap.

“The campaign is clearly going to have to come out with a position on it,” said Dean Baker, a progressive economist who met with economic advisers to Mrs. Clinton on other issues. “There is pressure on her to come up with a number.”