In a year of major Republican victories, the campaign to raise the minimum wage has been the rare success story for the left. Twenty states will see a minimum wage increase in 2015—more than half because state legislatures passed a law or voters approved a ballot initiative to do so.

Progressive advocates say other, broader reforms need to be in the spotlight as well. And the pressure to focus on middle-class incomes and wages will only grow as the 2016 election draws nearer, and candidates work to court the broader electorate.

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States with minimum wage increases in 2015 Hover over states to see their new wages Source: Economic Policy Institute

“Raising the minimum wage is great, but it’s not going to solve the problem of massive inequality in this country,” said Jennifer Epps-Addison, a Wisconsin labor organizer, speaking at an AFL-CIO event on Wednesday. “We need a living wage for everyone.”

The AFL-CIO has its own plans for moving forward. At Wednesday’s event, the labor union announced a new campaign in four states holding early presidential contests—Iowa, New Hampshire, South Carolina and Nevada—intended to hold 2016 candidates accountable for their position on income inequality and proposals that would help raise ordinary workers’ wages.

“Raising wages is the single standard by which leadership will be judged,” AFL-CIO president Richard Trumka said in a speech at the summit.

Whether or not she runs in 2016, Massachusetts Democratic Sen. Elizabeth Warren is likely to become a liberal standard-bearer on the issue. At the AFL-CIO event, she made it clear that her focus is squarely on raising middle-class incomes, mentioning the minimum wage only in passing.

“For more than 30 years, Washington has far too often advanced policies that hammer America’s middle class even harder,” Warren said. “Look at the choices Washington has made, the choices that have left America’s middle class in a deep hole.”

Warren’s suggested reforms were broad—infrastructure investment, corporate tax hikes and trade policy (an issue that’s pitted her against the White House). But the idea that drew the biggest reaction from the crowd was the one most directly connected to wages: workers’ right to be fully paid for what they earn.

“We believe in enforcing labor laws, so that workers get overtime pay and pensions that are fully funded,” Warren said, to big cheers and applause.

It’s an issue that could appeal to a broader swath of the public. “The minimum wage is about a floor, but it doesn’t raise wages for the vast majority of workers. Insuring basic workers’ rights enables wages to raise throughout the spectrum,” said David Madland, managing director of economic policy for the Center for American Progress.

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It’s also something that the White House is already preparing to act on, as it doesn’t need Congress to do so. Currently, only full-time workers who make up to $455 a week (or $23,660 a year) qualify for overtime pay, under federal labor rules that aren’t indexed to inflation and haven’t been changed since 1975. The White House is planning to move up the threshold, and liberals are pushing the administration to go significantly higher than the $42,000 level that the administration is reportedly eyeing.

Organizers are also pushing state legislatures and officials to fight wage theft by ramping up enforcement of existing labor laws. Some of the same big companies at the heart of the minimum wage fights, like McDonald’s, are also being accused of illegally underpaying workers. Congress and the federal government could both do more to increase enforcement of wage theft as well, advocates say—as well as the misclassification of employees as independent contractors, denying them benefits and other protections.

Such measures don’t get at the larger forces that have depressed U.S. wages for decades: technology, globalization and the decline of collective bargaining. In fact, some organizers believe that the focus on policy is altogether misguided. “We have to stop asking for politicians to pass policy reforms. Because we keep doing it, things haven’t changed. We need to ask them to help build the labor movement,” said Angie Wei, chief of staff of the California Labor Federtion. “Public policy ain’t cutting it.”

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But the minimum wage campaign has gained momentum largely because it’s focused on a concrete, pocketbook issue—and one that doesn’t require going through Washington to move forward. “Raising the minimum wage was and is the most immediate, essential, tangible requirement,” said Eric Hauser, an AFL-CIO spokesman. “There’s a lot of ground to make up, and a lot of places to make it up.”