President Obama wants to increase overtime eligibility to incomes of $50,440 a year. (Jonathan Ernst/Reuters)

Don Fox considers himself a good employer. The chief executive of a 896-location sandwich chain called Firehouse Subs gave his employees health-care coverage a year before it was required. But the Obama administration’s new overtime rules — which will make millions more salaried managers eligible for overtime pay — might be too much, even for him.

Right now, Fox’s salaried administrators and store managers don’t have to be paid time and a half above 40 hours a week if they make more than $455 per week. The White House said late Monday that it wants to double that threshold by next year. That might force Fox to convert salaried employees to hourly, or tell his salaried workers not to work more than 40 hours a week.

“What’s a real shame is that I’m in a position of having to penalize someone because they’re doing something they judge is best for their career,” Fox said. “Everything in this proposed rule is anti-American work ethic and culture.”

In a speech set for Thursday in Wisconsin, President Obama plans to explain that he’s trying to solve a problem. In 1975, the overtime rule covered 62 percent of the salaried workforce. Since then, inflation has eroded coverage to the point where only 8 percent of salaried workers qualify and the $23,660 a year cutoff is below the poverty line for a family of four.

The administration wants to increase eligibility to $50,440 a year, which is where the level would be if the cutoff had kept up with the cost of living. But with business owners such as Fox on the alert, the White House’s bid to directly raise Americans’ pay is running into a brushfire of resistance.

Obama signaled his intention to raise the overtime threshold in March 2014, as part of his efforts to go around a gridlocked Congress to bolster middle-class incomes that had remained stubbornly stagnant since the recession. Many employers had been able to load their low-level salaried professionals with extra hours, because it cost them nothing, rather than hire more workers to share the burden.

“With hourly workers, you can’t change the number of hours they work without paying them overtime,” said Dana Muir, a professor at the University of Michigan’s Ross School of Business. “It’s more that middle group that’s borne the pressure of the recession and then the expansion without hiring. So this is a big deal.”

Labor unions and progressive groups pushed hard for the change, and hailed the announcement as a step in the right direction. They said it might even prompt more hiring if employers avoid overtime by bringing on more workers. The change also should increase wages for women, minorities, younger people and the less educated, they said.

“Millions of America’s workers are one step closer to earning the overtime pay they rightfully deserve but have been systematically denied,” AFL-CIO President Richard Trumka said in a statement. “Working people called on President Obama to go bold, and his response will provide a much-needed boost to our entire economy.”

But business groups campaigned fiercely against the new overtime rule, both publicly and in Congress, with House Republicans holding a hearing in mid-June to criticize the idea. They said employers are likely to cut their managers’ base pay and benefits if they have to grant overtime, to keep compensation costs level without raising prices. They also might centralize oversight responsibilities at higher levels, which would cut down on the number of pathways to upper management and lead to more inequality, not less.

“The administration seems to be under the distorted impression that they can build the middle class by government mandate,” said David French, senior vice president for government relations at the National Retail Federation. “There simply isn’t any magic pot of money that lets employers pay more just because the government says so.”

In its proposal, the White House appears to have stopped short of imposing a requirement that some employers feared more: specifying the amount of time an employee has to spend on actual managerial duties to become exempt from overtime. That means businesses won’t have to tabulate the time a manager spends wiping tables or stocking shelves. For small businesses especially, counting overtime hours can be more onerous than paying higher wages.

“I want to pay my staff for their time,” said Joel Finkelstein, the owner of Qualia Coffee in Washington’s Petworth neighborhood. Two Qualia managers would qualify for overtime under the new policy. “I think the policy makes sense for larger businesses, but for small businesses, adding more documentation requirements is a disproportionate hassle.”

The rule will not take effect until after a 60-day comment period, and both sides are gearing up to flood the Labor Department with letters.

“It’s very difficult to stop a regulatory change, short of a statutory amendment,” said Lisa A. “Lee” Schreter, co-chairman of the wage and hour group at Littler Mendelson. “If the Labor Department reaches too far, perhaps you could see a coalition develop in Congress around certain changes.”

Amrita Jayakumar contributed to this report. An earlier version incorrectly said when Obama planned to give a speech in Wisconsin. This story has been updated.