Yesterday’s big flap over Hilary Rosen and Ann Romney triggered reams of analysis echoing the GOP spin that this was some kind of major “game changer” for Mitt Romney in overcoming the gender gap. Now that the facts of the matter have been established — Rosen does not work for the Obama campaign or the DNC, as Republicans falsely charged— we’re seeing some more level-headed and skeptical assessments.

Maeve Reston, for instance, points out that the Rosen battle is somewhat less important than the actual issues and positions Romney has embraced that could continue to alienate women:

The more crucial question is what the toll has been of his sometimes harsh rhetoric on issues of concern to moderate women, like budget priorities, immigration and the nation’s social safety net.

On those topics, Romney has at times boxed himself in. He has pounded Obama for job losses among women during his tenure, yet rarely acknowledged that many of those cuts were in government jobs that would be sliced further under his proposals, which would shrink government employment by 10%.

Though middle-of-the-road female voters tend to be more concerned than conservative women about maintaining the nation’s social safety net and expanding healthcare access, Romney has vowed to repeal Obama’s healthcare law, rein in the growth of programs like Medicare and get rid of government aid to Planned Parenthood....

In his haste to show his credentials as a fiscal conservative, Romney also has repeatedly criticized the president for promising voters “free stuff” — by implication trashing programs like education subsidies that are popular among women voters.

Meanwhile, Politico takes a longer view this morning of the battle over women, noting that Democrats remain confident that the larger showdown over who is really representing the interests of female swing voters is one they will win. Yesterday’s events don’t change the tangential matter of Romney’s actual positions on issues that matter to women, and indeed, if anything, the furious effort by the Romney campaign to change the subject to Rosen’s comments may underscore this.

It’s also going to be interesting to see whether this is really such a big victory for Republicans, now that Obama has weighed in by invoking his own mother’s hard work and calling on people to refrain from attacking spouses, including Ann Romney herself.

* Obama ratcheting up pressure on Romney over tax returns: Today the Obama campaign and Joe Biden will be releasing their tax returns and posting them on the Web, to increase pressure on Romney to release his own. Meanwhile, the Obama-allied Priorities USA Action has released a new Web video introducing the “Romney Rule.”

The multi-front push is about highlighting Romney’s personal profits from the tax code Obama’s Buffett Rule would undo — reinforcing the message that Romney is the walking embodiment of the ways the system is rigged for the rich and against the middle class.

* Obama re-elect reality check of the day: I fully agree with Charlie Cook on this: Predictions that Obama will coast to victory are ridiculous, and all signs are that this will be an extremely close election that will turn on the unpredictable, particularly concerning the economy.

* It all turns on the economy: Relatedly, Larry Bartels has an interesting piece up digging into history to demonstrate that the next president may be dictated by income growth this year and nothing else .

Bartels notes that the economy’s performance throughout Obama’s term could prove largely irrelevant, and public perceptions of the direction of the economy this fall could decide all.

* Romney campaign presents no evidence of Obama “war on moms”: The Romney campaign held a conference call to argue falsely that the Hilary Rosen flap proves tObama administration is disrespecting stay-at-home moms. But as today’s Post story on the flap points out:

“This administration would do well to stop disrespecting stay-at-home moms and listen to them,” said Penny Nance, president of the conservative organization Concerned Women for America. But when pressed by reporters for examples of the president or his administration showing disrespect for mothers who work at home, the Romney surrogates did not provide any specific examples.

* Questionable media coverage of Rosengate: By contrast, the New York Times’s big story on yesterday’s battle tells you in the second paragraph that Rosen has “ties” to Obama, whatever that means, and doesn’t tell you until the 22nd paragraph that Dems pointed out that Rosen doesn’t have any role with the campaign. And even then it’s presented as he-said-she-said.

* What really matters in the battle for women: Jess McIntosh, of EMILY’s List:

“When it comes to connecting with women, it’s not just an optics problem — it’s a substance problem. Even if Romney could put a really great spin on his anti-woman regressive policies, they would still be anti-woman regressive policies. And despite what the GOP may think, women notice that.”

* No, Paul Ryan is not serious: The Bloomberg View editorial board still can’t get Ryan to tell them which tax deductions for the rich he’d eliminate to pay for his plan’s enormous tax cuts for the rich. Which is to say, again, that Ryan has not offered a serious plan to cut the deficit, despite his ongoing pose as a very serious prophet of doom about the threat the deficit poses to American life as we know it.

* No, Chris Christie is not serious: Paul Krugman uses Chris Christie’s opposition to the New Jersey-New York tunnel as a jumping off point for a riff about how Republicans warning about the deficit burdening future generations are the ones who are really selling out the country’s future, by refusing to countenance government action to secure it.

The big con here is that the very same GOP politicians posing as the ones making “tough choices,” as Ryan keeps doing, are actually the ones who are peddling an easy-to-swallow bill of goods to the base.

* And it’s all about Elizabeth Warren’s likeability: A smart piece from the Boston Globe’s Glen Johnson about how the ban on outside spending in Massachusetts has created a strategic dilemma for Scott Brown: How can he drive up Elizabeth Warren’s negatives, without doing the dirty work himself?

As I noted recently, the expected presidential-election-year will likely mean the race will hinge less on Brown’s successful packaging of himself as independent and a “regular guy” and more on whether Warren clears a basic likeability threshold.

What else?