Today’s New York Times/CBS poll contains awful numbers for Obama. His approval rating is at an all-time low of 41 percent. On the economy, that number is even lower, at 39 percent. The right-track-wrong-track numbers are 29-63.

And yet...

In the head to head matchup with Mitt Romney, Obama has made, and held, inroads with key voter groups that abandoned Democrats in 2010. Chief among them: Women.

The poll finds Obama beating Romney by 49-41 among registered independents. That is driven by independent women, who prefer Obama by double digits. Among women overall — who split between Republicans and Dems in 2010 — Obama is favored by half, versus 39 percent for Romney.

Interestingly, the same poll finds questionable support for Obama on the birth control coverage mandate. Fifty one percent say employers should be allowed to opt out of covering birth control based on religious or moral objections. (Yesterday’s Post poll found majority support for Obama’s position.)

But here’s what’s intriguing: The poll also finds that voters view the issue the Dems’ way, with a majority saying this fight is about women’s health and women’s rights, and not about religious liberty. Note this quote from a follow-up interview with an independent woman:

“They take a stand on keeping big government out of our lives, but then they want government to take over our private lives. It bothers me that with so many problems and issues in this world, the Republican candidates can only focus on religious issues.”

The economy is likely to be the main driver of this election. Romney will have another chance to introduce himself to swing voters after the primary. Head-to-head matchups are not terribly important at this stage. But if this election is going to turn heavily on suburban and independent women, the GOP’s rejoining of the culture wars — and the relitigation of health reform around the law’s benefits for women in particular — could help define the contrast between the parties, and the GOP’s values, priorities, and vision for the future. That’s what Dems are betting on, anyway.

* Culture wars in full swing: MoveOn is releasing a new ad on national cable that features women themselves voicing all the lovely things that Rush Limbaugh, Rick Santorum and other conservatives have said about birth control, abortion, and rape.

“We women have a serious problem with the Republican Party. We’re women. We vote,” the ad concludes, demonstrating that outside groups on the left see the rejoined culture wars as a way to exacerbate the gender gap in Dems’ favor, in an election that is supposed to be about the economy.

* Terrible numbers on gas prices: This from the NYT/CBS poll is also key:

Is the price of gasoline something a president can do a lot about, or is that beyond any president’s control?

Can do: 54

Beyond control: 36

The danger is that rising gas prices could stomp on the recovery, sapping Obama’s credit for it, and perhaps become a proxy for general impressions of ineffectiveness on the president’s part.

* Gas prices bedevil helpless politicians: A roundup of expert opinion on just how little presidents can do about gas prices — and how little regard for that fact voters have historically shown. That said, the evidence is thin that gas prices actually have a meaningful impact on presidential elections.

* Will jobs numbers help Obama? An interesting point from Nate Silver: Gallup’s tracking has Obama at 49 percent, and unlike the NYT and WaPo polls, Gallup’s polling all was done after the relatively good February jobs report.

* Get ready for the next Ryancare battle: With Paul Ryan set to introduce a new version of his Medicare plan, DCCC chair Steve Israel publishes an Op ed arguing that Republicans aren’t actually interested in cutting spending but rather are using Medicare to pay for tax cuts for the wealthy.

“Budgets are about priorities, and the Republicans priority is that millionaires come first and seniors’ Medicare comes last,” Israel says, essentially spelling out the blueprint Dems hope will define the 2012 elections.

* Dems hit Romney over Medicare: The DNC is out with a new Web video highlighting Romney’s announcement yesterday that he won’t enroll in Medicare (he can afford not to) and hitting him for supporting Paul Ryan’s plan while favoring tax cuts for the rich.

The battle over Medicare, which is likely to escalate when Ryancare 2.0 hits, is perhaps the first good test case for whether Romney’s need to embrace unpopular positions in the primary will damage him among core general election constituencies.

* Romney is lucky enough not to need Medicare: Relatedly, Jonathan Cohn has a nice piece connecting Romney’s wealth to his willingness to support a plan that would put middle class seniors at financial risk, including this conclusion: “you have to wonder whether his affluence blinds him, or at least desensitizes him, to the threat medical expenses can pose — and the difficulty older Americans traditionally have in the private insurance market.”

* Will Romney gain momentum towards nomination? With the Mississippi and Alabama primaries set for today, the question remains whether something will trigger a stampede of support into the Romney camp, effectively ending a primary that would otherwise drag on well into June. Sean Trend pours cold water on the “stampede” theory.

Also: If Newt Gingrich loses both, will he drop out, finally giving Rick Santorum his head-to-head matchup against Romney?

* And is GOP pushing austerity in hopes recovery will fail? Mike Tomasky offers a political prism through which to view the upcoming budget war: Republicans desperately want more public sector jobs losses to keep unemployment high:

By opposing everything Obama wanted with such ferocity; by saying all those thousands of times that he had no clue about the economy; by sending out a parade of presidential candidates, from the semi-serious to the clown posse, all of whose central criticism of Obama is that he killed the economy — in all of these ways the party has more invested in economic failure than any out-party I can remember in my lifetime. Its best hope for now is gas prices, but even they eventually get lower, usually by late summer. Beyond that, all the GOP has to rely on is Mitt Romney’s unstoppable charisma.

If this is true, it becomes all the more difficult to understand why Dems like Steny Hoyer are venturing on to “grand bargain” turf.

What else?