MOUNT VERNON, Iowa (Reuters) - President Barack Obama bounced off a strong debate performance to target women voters on Wednesday with a dig at Republican Mitt Romney's comment that he received "binders full of women" for cabinet jobs when he was governor of Massachusetts.

Obama and Romney are eager to win over women in swing states such as Iowa and Ohio, where the Democratic incumbent was campaigning a day after his energetic debating rejuvenated his re-election campaign.

During the second presidential debate on Tuesday night, Romney noted he had been given "whole binders full of women" when looking for candidates for his cabinet. The awkward phrase quickly took off in social media and critics suggested the remark showed Romney had few women in his inner circle.

"We should make sure all our young people, our daughters as well as our sons, are thriving in these fields," of science, technology, engineering, and math, Obama told a cheering crowd of some 2,000 people in Mount Vernon, Iowa.

"I've got to tell you, 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," he said. "And when young women graduate, they should get equal pay for equal work."

Obama also hammered Romney for wanting to cut funding to Planned Parenthood, a women's health organization.

With his sleeves rolled up and his tie loosened, Obama seemed energized by his own debate performance, which the campaign hopes will erase memories of his listless appearance in the first debate that gave a bounce to challenger Romney in opinion surveys.

Reuters/Ipsos polling data showed Obama's support slipping among women after the president's first debate.

Obama, however, made it clear he was not on a victory lap.

"I'm still trying to figure out ... how to get the hang of this thing, debating," he said. "But we're working on it. You know, we'll keep on improving as time goes on."

(Reporting by Mark Felsenthal, writing by Jeff Mason; Editing by Alistair Bell and Doina Chiacu)