Whither the love for Barack Obama?

Coming off the one-two punch of disheartening jobs numbers and a failed attempt to tar Mitt Romney as a vulture capitalist, the Obama campaign is under fire. Its clumsy Bain attacks were blunted by friends and frenemies alike: Cory Booker’s nausea and Bill Clinton’s blessing of Romney’s “sterling” business record had Obama boosters reaching for the Rolaids.

But Obama can still find solace in the arms of female voters. Reports of Romney’s luck with the lady vote have been greatly exaggerated. Much ado was made of a recent ABC News/Washington Post poll showing Romney gaining substantially among women voters.

However, the gains are merely among Republican women.

“What we are seeing is GOP women who had been previously spread among many candidates coalescing around the presumptive nominee,” Debbie Walsh, director of the Center for American Women and Politics, told me. “Romney is picking up who he should be picking up.”

In other words: Republicans are supporting the Republican candidate. The sky is also blue.

Obama still has a large lead among women overall: according to Gallup’s May 6 poll, Obama leads Romney among women 49-42 percent. It’s the independent women who are being watched closely by the experts. Walsh said she has not noted any statistically meaningful change in the president’s support among this cohort.

“During the Republican primary, the independent women had really fallen away from Mitt Romney, and we haven’t seen them bouncing back,” Lanae Erickson of the centrist think tank Third Way told me. “There was a big change around January with the contraception debate, and then in the spring Romney didn’t distance himself from the extreme things being said by other GOP candidates.”

In the Gallup/USA Today battleground poll, Obama was down by 5 among independent women in December and up by 14 by March.

Senate Democrats are doing their best to keep women in the Obama column. They pushed through a high-profile equal-pay bill that was blocked by Republicans on Tuesday. “It is incredibly disappointing that in this make-or-break moment for the middle class, Senate Republicans put partisan politics ahead of American women and their families,” Obama said in a statement after the vote.

For their part, Republicans argued that ensuring equal pay for women was a “job-killing burden” on business. Good luck with that one.

Indeed, the Dems couldn’t have scripted it better: there is now another arrow in their “war on women” quiver. Unlike some of the recent skirmishes, this one may really matter. The economy is the No. 1 issue among all voters, and women are more likely to be economically vulnerable and rely on the government to provide a safety net. Arguing, as Sen. Mitch McConnell did Tuesday, against the pay-equity bill because there is too much litigation in the country, is pretty weak tea. Maybe if employers stopped discriminating against women, women would stop suing them for discrimination. Just a thought.

“One of the things we saw among independents is they see the Republican Party as much more extreme as they used to,” said Erickson of Third Way’s polling. “To the extent Obama can link Romney to congressional Republicans, those independent women will be with Obama. Romney needs to distance himself from some of the things that make the GOP seem so extreme” if he wants to win over these voters.