Mitt Romney’s second-in-command when he was governor of Massachusetts and a coalition of women's groups rallied Wednesday behind the Republican presidential nominee in the face of a rapidly expanding Internet phenomenon poking fun at his "binders full of women."

The supporters said Romney, indeed, asked for and received binders with names of potential female candidates for high-level posts -- backing up his claim in Tuesday night's debate that as governor he had reached out to women's groups because he was dissatisfied with the mostly male applicants for jobs in his administration.

Romney's anecdote, in which he recalled receiving "binders full of women," was part of the Republican's efforts to appeal to undecided female voters, a voting bloc that could swing the election.

President Obama once held a double-digit lead with the group. But a recent Gallup survey shows the president just 6 percentage points ahead of Romney among likely women voters.

Kerry Healey, Romney’s former lieutenant governor, said 10 of the 20 top positions in the administration were filled by women -- more than any other state in the nation.

More On This...

“Mitt Romney had a commitment to making sure women were properly represented in his administration,” Healey, now a Romney campaign adviser, told Fox News. She also explained the initiative was part of a campaign promise.

But Romney's choice of words Tuesday night – the “binders full of women" – sparked an almost immediate wave of social media parodies and more talk about the issue on the campaign trail.

“We don't have to collect a bunch of binders to find qualified, talented, driven young women ready to learn and teach in these fields right now,” Obama said at Cornell College in Mount Vernon, Iowa.

Vice President Joe Biden, at a campaign stop in Greeley, Colo., said: "When Governor Romney was asked a direct question about equal pay, he started talking about binders. Whoa. The idea that he had to go and ask where a qualified woman was, he just should have come to my house. He didn't need a binder."

The Romney campaign has released a YouTube ad in which three former Cabinet member talk about the former governor’s commitment to women.

“He totally gets working women, especially working women like myself who had two young kids,” Ellen Roy Herzfelder, a former state secretary of environmental affairs, says in the 30-second ad.

The Massachusetts Government Appointments Project -- which began before Romney was elected in 2002 -- acknowledged the number of women in top positions increased under Romney.

According to a survey conducted by the University of New York in Albany at the time, the Romney administration had more women in senior leadership positions than any other state in America.

Fox News' Nick Kalman contributed to this report.