It took just four words by Republican candidate Mitt Romney to wreck the work he and his campaign staff have done in the last two weeks to portray him as a strong and likeable candidate and restore the reputation for blundering he built up in the early months of the campaign.

The former governor of Massachusetts was answering a question during the second televised presidential debate about inequality at work and fair pay for women when he said he had "binders full of women". Puzzled netizens ran amok.

Three Twitter accounts named after "Romney's Binder" quickly picked up several thousand followers and the hashtag #BindersFullofWomen became a top trend on social media

President Barack Obama joined in the fun, tweeting: "Mitt Romney still won't say whether he'd stand up for equal pay but he did tell us he has binders full of women."

"Ann Romney is rifling through the house trying to find Mitt's little black binders full of women while cursing under her breath," was tweeted by Top Conservative Cat

"You know who else has binders full of women? Serial killers," wrote Stephen Blackmoore.

"I want a binder full of chicks. Get it?" tweeted an account dedicated to TV puppet Big Bird, which has become the symbol of Romney's threat to cut funding for public broadcasting in the US.

Romney's "binder" comment came as he was telling the audience at Hofstra University in Hempstead, New York, an anecdote about his times as governor of Massachusetts in 2003 to show that he cared about equal opportunities in the workplace.

"I had the chance to pull together a [political] cabinet and all the applicants seemed to be men," Romney recalled. "And I went to my staff and I said, 'How come all the people for these jobs are men? And so we took a concerted effort to go out and find women who had backgrounds that could be qualified to become members of our cabinet. I went to a number of women's groups and said, 'Can you help us find folks', and they brought us whole binders full of women."

Romney said that after going through the binders, his cabinet contained more women in senior leadership positions than any other state in the US.

"One of the reasons I was able to get so many good women to be part of that team was because of our recruiting effort. But number two, because I recognised that if you're going to have women in the workforce that sometimes you need to be more flexible. My chief of staff, for instance, had two kids that were still in school," Romney added.

The speech raised feminist eyebrows as observers found it hard to believe that in 2003, when Romney was forming his cabinet, it was so hard to find qualified women.

Romney also gave the impression of holding a backward view of families and women's role in society by suggesting that the family and domestic care were the jobs of women.

In reply to the same question, Obama said: "Women are increasingly the breadwinners in the family. This is not just a women's issue, this is a family issue, this is a middle-class issue, and that's why we've got to fight for it."

The president has held a strong lead among women voters since the beginning of the electoral campaign, partly because of Romney's conservative views on abortion and contraception.

However, a recent poll showed that the Republican candidate was gaining ground among women voters especially in key swing states.