But Tammy McCutchen, one of the architects of the Bush administration’s increase, said she was pleased that the department had set the threshold at about the 20th percentile of earnings for salaried workers in the South — in line with where she and her colleagues had set it in 2004.

“I think that’s what they had to do in light of the Texas court decision,” said Ms. McCutchen, a lawyer at the management-side firm Littler Mendelson. “Anything higher would have been subject to challenge again.”

Many employers and business groups argued that while the 2004 threshold was in need of an increase, the magnitude of the Obama change was unreasonable.

Some argued that it would significantly increase costs for employers, who would either have to pay out hundreds of millions more in overtime or raise workers’ salaries above the new threshold to avoid paying additional overtime. Many critics also said salaried workers would suffer a loss of status by having to account for their time the way hourly workers do.

The Obama administration argued that its proposal was modest by historical standards, noting that it would make fewer than 40 percent of salaried workers eligible for overtime pay based on their salaries, far less than the percentage who were eligible in 1975.

Even so, it estimated that more than four million workers would gain the right to overtime pay under its rule.

Other skeptics argued that the change would have little impact because employers would lower the base wage of people who work significant overtime hours, leaving their total pay, including wages and overtime, roughly unchanged.