Mitt Romney, the newly minted presumptive Republican presidential nominee, has turned his attention from beating his GOP rivals to winning over a key bloc of voters -- women.

But while Democrats trumpeted charges that Republicans are waging a "war on women," Romney's problems are much more complex, according to political observers, as his laser focus on the economy and budget deficit has left some women questioning whether Romney understands the wide range of their concerns, from education to health care.

Romney's newfound focus on women fits with his pivot to general election mode, as he's facing a nearly 20 percent gap among women compared with President Obama in a number of battleground states. In an indication of how pivotal women may be in the November election, the Obama and Romney campaigns on Wednesday spent what was effectively the first day of the general election trading accusations on women's issues.

The Romney campaign believes its clearest path to winning over women is to continue Romney's focus on the economy, highlighting what it's portraying as a hemorrhaging of jobs during Obama's watch. Others question whether the tact will work.

"I think Romney's problems with women are emblematic of his problems with everyone," said an adviser from Romney's 2008 presidential bid, granted anonymity to speak about her former boss. "It's not about social issues; it's not about contraception; it's about a guy who women -- at least so far -- don't think entirely gets them. It's that empathy factor."

Romney's campaign didn't help him Wednesday when aides fumbled a reporter's question about whether Romney supports a law enacted under Obama mandating equal pay for women. A campaign aide didn't immediately know whether Romney supported the measure.

The Obama campaign seized immediately on the miscue.

"If he is truly concerned about women in this economy, he wouldn't have to take time to 'think' about whether he supports the [act]," Lilly Ledbetter, the woman for whom the pay equity law is named, said in a statement distributed by the Obama campaign. "This act not only ensures women have the tools to get equal pay for equal work, but it means their families will be better served also."

Romney, meeting Wednesday with a half-dozen female business owners in Connecticut, accused Democrats of inventing a so-called war on women.

"I was disappointed in listening to the president when he said, 'Oh, the Republicans are waging a war on women,' " Romney said. "The real war on women is being waged by the president's failed economic policies."

Romney's campaign claims that nine of every 10 jobs lost during Obama's first term were held by women. Democrats disputed that, saying it fails to account for the jobs lost before Obama took office. Those jobs were held primarily by men and, if counted, would drastically reduce the percentage of jobs lost by women.

Republicans insist Romney's focus on the economy will eventually win over women.

"It's a solid strategy to tie Obama's fiscal woes with many of the issues that are affecting women today, especially college-educated and professional women, who seem to be the swing vote this cycle," said GOP strategist Brian Donahue. "Women, just as much as men, are deeply concerned with the current state of our economy."