While Democrats usually support increasing the minimum wage, these politicians are hearing from Washington’s waiters and bartenders, who’ve said the “raise” offered by Initiative 77 would actually reduce their earnings.

Ms. Bowser signed legislation in 2016 raising the District’s minimum wage to $15 an hour by 2020. The D.C. Council unanimously supported the increase, but also preserved an hourly “tipped wage” of $5 for servers and bartenders. Forty-three states and the District of Columbia permit restaurants to pay a lower base wage to tipped employees, provided tips bring their incomes up to at least the regular minimum wage.

Tipped employees—who can earn far more than $15 an hour in total pay—were the driving force behind preserving the tipped wage. They cautioned the council that eliminating it could lead employers to lay off workers due to higher labor costs.

That logic convinced the D.C. Council to preserve the tipped wage, but it wasn’t acceptable to labor groups that would prefer to see cash tips eliminated altogether in favor of flat minimum wages. The New York-based nonprofit Restaurant Opportunities Centers United and its 501(c)4 arm, ROC Action, funded the signature drive to put Initiative 77 on next week’s ballot. The group views the elimination of the tipped wage in Washington and elsewhere as a first step “in getting to no tips.” As Diana Ramirez, director of ROC-DC, explained, “You can’t do payroll deductions”—that is, unions can’t dip into cash pay to collect dues.

The activists pushing for a flat wage have a big problem: Most tipped employees aren’t interested in a no-tipping future. A 2016 survey of several hundred tipped workers by industry publication Upserve found that 97% preferred the current system to a salaried alternative. New York restaurateur Danny Meyer learned this lesson the hard way after he embraced a “gratuity-included” model at well-known establishments like Union Square Cafe and Gramercy Tavern. In an interview earlier this year, he acknowledged losing as much as 40% of his veteran staff because of a sharp drop in their overall pay.

Not surprisingly, ROC has struggled to find tipped employees in Washington who embrace its cause. A pro-Initiative 77 website features only three video testimonials from employees who want the change. Meanwhile, tipped restaurant employees who are against the measure have made their voices heard. The Washington Post identified them as the “loudest opposition” to the initiative’s passage. Hundreds of restaurant workers packed a May meeting with elected officials to voice opposition. One councilman observed: “There’s not a restaurant I go to where . . . all the waiters don’t surround me and say, ‘Please don’t let this go into effect.’ ”

Local restaurants have helped support a “save our tips” campaign to amplify the employees’ concerns, but “save our jobs” might be a more appropriate tagline. Recent evidence from the Bay Area suggests that each dollar increase in the minimum wage in a market without a tipped wage causes a 14% increase in closures for median-rated restaurants. These aren’t struggling eateries on the edge of going bust. In Washington, that median rating—3.5 stars on Yelp —includes some of the most popular local restaurants.

National Democrats will be closely watching next week’s vote, but they could end up taking away the wrong message. Elimination of tipped wages is part of the Democratic platform. Sen. Bernie Sanders’s proposed Raise the Wage Act, which would boost the federal minimum base wage for tipped workers by 600%, has strong Democratic support in both chambers of Congress.

A mandated pay hike of this magnitude may be a winner in progressive fantasy land, where no economic policy decision ever causes a business to shut its doors or lay off workers. In the real world, however, most bars and restaurants operate on extremely thin margins. Servers and bartenders know this and are eager to keep their jobs and income. Thousands rallied recently in New York and Michigan against similar efforts that would put their tips at risk.

In a federal fight over the tipped wage, the party of “working people” may find itself the subject of a revolt from those it claims to help.