House Majority Leader Eric Cantor of Va., left, accompanied by House Speaker John Boehner of Ohio, speaks during a House Republican Leadership news conference, April 16, 2013, on Capitol Hill in Washington. Photo Credit: Jacquelyn Martin/AP Photo

Just in time for Mother's Day, House Republicans today successfully pushed through a bill aimed at mending the party's ailing standing with women voters.

The Working Families Flexibility Act, a bill that allowed employees to take time off instead of overtime pay, passed in the House of Representatives Wednesday night and was billed as a "straight-up answer to the problems that working moms and dads are facing," according to House Majority Leader Eric Cantor, R-Va.

Led by the bill's co-sponsor, Rep. Martha Roby, R-Ala., a mother of two, the legislation aims to give private-sector employers the same ability that government workers have to take either comp time or overtime pay.

"This is about choice. This is about flexibility," Roby said at a news conference Tuesday. "I guess my question would be, if it's good enough for government employees, why isn't it good enough for the private sector?"

Coming on the heels of a presidential election in which Republicans suffered the worst loss of women voters in the 60-year history of the Gallup survey, it's clear why the Republican Party would see this as a chance to appeal to women voters and shore up their base.

And it comes at a time when there is more public debate, and little clarity, about what working women want and need: more money or time.

While Facebook COO Sheryl Sandberg has exhorted women to "lean in," negotiate for higher salaries and push for fair pay, she has also called on employers to make workplace policies fairer for women who are also mothers by allowing flexible work options.

The problem, say labor and some family advocate groups like the National Partnership for Women and Families, is that this bill allows businesses to pay women less under the guise of giving them more flexible work options.

"What employers are trying to do here, and it's not a great secret, is they want to get out of paying overtime for employees and work them more than 40 hours a week and then tell them you can take comp time that's available to you," Rep. Donna Edwards, D-Md., said during a conference call Monday. "Only the fact is that that comp time, that compensatory time, won't be available to them at their leisure."

Proponents of the legislation, including the U.S. Chamber of Commerce and the Society for Human Resource Management, which represents employers, say it gives workers, especially parents, the ability to take time off to be at parent-teacher conferences or doctor's appointments.

Here's how it's supposed to work: A person who works more than 40 hours a week can arrange with their employer to take that time in the form of compensatory (comp) time, instead of overtime pay. Each hour of extra work is worth an hour and a half of time off.

According to the bill, agreeing to time off instead of overtime pay can't be a condition of employment, and the employee can also choose to take the money instead of time at any point.

Employers can deny requests for time off at any time, as long as they can show that it might "unduly disrupt the operations of the employer," according to the bill.

And just as it is for the government, the bill would undoubtedly be a cost-saving measure for businesses as well.

Today's came down along partisan lines with only three Democrats joining 220 Republicans in approving the measure, mirroring the fate of similar pieces of legislation that were taken up in the 199's but failed to become law.

What's next for the bill? Most likely nothing, if Democrats have anything to say about it.

The White House has said it would potentially veto the bill if it ever got to President Obama's desk.

And there is no indication that it ever will, as long as Democrats remain in control of the Senate.

"This week we gave mothers not a very good gift: more work, less pay. Happy Mother's Day? I don't think so," said House Minority Leader Rep. Nancy Pelosi (D-Calif.) at a press conference today. "The bill that gives less flexibility to working people, more discretion to their bosses."

ABC News' John Parkinson contributed to this report.