The party lost women by 10 points in the 2012 presidential election and by even wider margins in some congressional races. It’s alleged “war on women” pervaded an election Republicans had hoped to frame around the lagging economy. Voters equated the party with a group of “stodgy old men,” as the national party chairman recently characterized the thumbs-down.

Something had to give. And the onus of combating this negative narrative fell on the only Republicans in power: those in the House of Representatives leadership. Washington Rep. Cathy McMorris Rodgers occupies one of those leadership posts; House Speaker John Boehner often addresses the press with women lawmakers by his side; and the party’s House campaign arm is aggressively courting female candidates and warning recruits about Akin- and Mourdock-like mistakes. (Their comments on rape and pregnancy torpedoed what looked like sure-fire victories.)

Majority Leader Eric Cantor also has been leading the rebranding effort and is guiding a series of bills he says are designed to “make life work” -- a theme he outlined in a speech earlier this year at the American Enterprise Institute about how his party can broaden its appeal. The House passed the Skills Act, the first in the series that involved job training and resources for employers, in March (North Carolina Rep. Virginia Foxx introduced the measure). But the next one flopped -- a health care measure that would have taken money from Obamacare to create an insurance pool for people with pre-exiting conditions. Conservative members and outside groups viewed the bill as an expansion of Obamacare and Cantor yanked it after failing to garner enough support. 

This week, the House passed the Working Families Flexibility Act, which would give private sector workers the option of swapping overtime pay for time off. And that brings us back to Martha Roby, the Alabama congresswoman Cantor approached to lead the way in selling the bill. The 36-year-old Republican, a working mother of two, was a perfect fit for the chore, aides say.

“As a mom that wants to be there for the PTA meeting or for the swim meet, to have that flexibility is huge,” Roby told CBS’s “This Morning” on Wednesday. “The great thing about this is that it’s up to the employee to determine how to use it because it’s your time. You get to decide how to use your time.”