NEW YORK — Retailers and manufacturers blasted President Obama’s plan to make more Americans eligible for overtime pay, saying the move would stunt workers’ careers and cost companies billions.

The National Retail Federation says Obama’s proposed rule change to greatly increase how many salaried employees can claim overtime would force companies to use more part-time and entry- level workers. Businesses also may offer fewer promotions and convert salaried employees to hourly to avoid raising their pay, the NRF said.

“The proposal is going to cost billions of dollars,” said Neil Trautwein, vice president for the NRF, the industry’s largest trade group. “It’s going to limit advancement opportunities, and ultimately it will reduce employee benefits.”

The NRF said the move, which would go into effect next year, would cost $9.5 billion annually if retailers and restaurants implemented the change without making adjustments. Total payroll expenses for all 25 million workers in these industries was $545 billion in 2012.

Obama’s plan would make workers who earn a salary of as much as $970 a week, or about $50,000 a year, eligible to claim overtime under the Fair Labor Standards Act. The current threshold is $455 a week, or about $24,000 a year, which is below the poverty line for a family of four. The change would benefit 4.68 million people, the White House said Tuesday on its website.

An analysis by the Economic Policy Institute showed large increases in the percentage of workers that would be eligible for overtime if the threshold were raised to a level similar to Obama’s proposal. Among retail supervisors, about 56 percent would be covered, up from 8 percent. The group calculated comparable jumps for restaurant managers, insurance clerks and customer-service representatives.

Major chains already were under pressure to boost hourly wages for their lowest-paid workers. Many, including McDonald’s and Wal-Mart, have done just that. Now Obama says he wants to boost the pay of middle management. Of those affected, a majority have college degrees, are women and are older than 35, the Department of Labor said.

“A hard day’s work deserves a fair day’s pay,” Obama wrote on the White House website. “That’s at the heart of what it means to be middle class in America.”

The NRF and other trade groups aren’t buying it.

“The Department of Labor announced the demotion of at least 5 million Americans,” Joe Trauger, a spokesman for the National Association of Manufacturers, said in a statement. “This proposed regulation is another in a long list of regulatory roadblocks to healthy and robust economic growth and job creation.”

The Retail Industry Leaders Association, another trade group, also slammed the plan. The American Apparel & Footwear Association said it didn’t have a position on the rules.

The changes may be extra hard on small and mid-size businesses, said Martin Mucci, chief executive officer of Paychex Inc. The Rochester, New York-based company provides payroll and human-resources services for almost 600,000 firms.

“We certainly want to make sure employees are paid fairly, but I think this is going to place a burden on a broad group of businesses,” Mucci said.

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