Employers generally don’t like being told to raise wages, so it was not surprising that various employers, including businesses and nonprofits, have objected to a rule change proposed by the Obama administration.

Read: Employers aware, concerned about overtime status

That rule change would dramatically expand the number of employees who would be required to receive overtime pay when they work more than 40 hours a week.

The proposed rule would more than double the salary threshold above which a worker could be exempt from overtime pay from $23,660 to $50,440.

But one employer group that has had a tough time coming to a position on the issue is the American Network of Community Options and Resources. ANCOR is an association of employers that provide care to people with intellectual disabilities.

"When we brought this issue to our board, the response was emphatically, 'Yes, we want to pay the people that work for us what they're worth,' " Gabrielle Sedor, chief operating officer of ANCOR, told NPR.

But Sedor says that after some number-crunching she is hesitant to support such a dramatic change in compensation policy. And considering that the groups providing the services get a large percentage of their funding from Medicaid, she said they will likely respond to the policy by asking for more money from the feds. 

Providers will spend an additional $1 billion a year on overtime pay on employees who currently make between the current threshold and the proposed one, according to a study the group commissioned. The study based that estimate on the average salary of a worker making between the two thresholds –– $37,050 –– and the five hours of overtime that employers reported their employees work.

In a second scenario explored by the study, employers would avoid additional overtime payments by instead raising the salaries of their workers by an average of $13,000. That would cost the organizations an estimated $1.86 billion.

Of course, the actual response from employers will include a mix of the two scenarios, in addition to a third strategy: cutting hours.

"What's most troubling to me is that over 20 percent (of member organizations) thought that they would be forced to reduce services, and that's a real challenge, because in every state the need for services to people with intellectual disabilities is growing," Sedor said.