WASHINGTON — There was Sarah Palin again on Monday, assuring Sean Hannity on Fox News that she was not going to be silenced, no matter what abuse might come her way.

“Other people are facing much greater hardships and making greater sacrifices than I am in just engaging in debate,” said the woman who reportedly made $250,000 per episode of her recently concluded reality show.

She added, several times, “This isn’t about me.”

A lot of Republicans in Washington certainly wish that were the case. But as the new House majority begins its push this week to scale back the Obama agenda, it seems that the president now has, in Palin, something he badly needed after a punishing election season: the ideal political foil.

In a new poll from ABC News and The Washington Post, only 30 percent of respondents approved of Palin’s highly publicized response to the shootings that gravely wounded Rep. Gabrielle Giffords and killed six others, while 46 percent said they disapproved. By contrast, 78 percent approved of how President Barack Obama handled the incident, compared with just 12 percent who did not.

All of which suggests that the events of the past 10 days have complicated things for Republicans who are intent on getting back to business this week, starting with a push to repeal the new health care law. Speaker John A. Boehner and his lieutenants are clearly trying to learn the lessons of the last Republican takeover, in 1995. They are determined to focus on their substantive disagreements with Obama, presenting a reasoned alternative to his agenda rather than getting dragged into the kind of personal attacks that ultimately worked against the party back then.

But since the first minutes after the shootings, Palin (and not Boehner) has again been the most-talked-about Republican in the country. And Palin represents exactly the kind of culturally conservative critique of Obama that her Washington colleagues would like very much to play down at the moment. Her grievances are based less in the particulars of policy than they are in the caricatures and cultural divisions of the last political era — effete Easterners versus rugged Westerners, wine-drinkers versus beer-pounders, Ivy League lawyers versus Bible-brandishing activists.

Palin got into politics by taking on the Republican machine in Alaska, and she continues to occupy the role of an anti-establishment figure, someone who cannot be controlled by her party’s top officials. In fact Palin seems bent on asserting her own claim to the party’s leadership, putting herself on par with Boehner and his Senate counterpart, Mitch McConnell.

“In our system of government, the party that does not have the presidency does not have a recognized leader,” said Mike DuHaime, a top Republican strategist. “She’s one of the very few who tries to fill the void.”

For the White House, it would seem, this is a hopeful development. That’s because every modern president, and especially one who finds himself confronting divided government, needs the kind of critic who can remind the public of why he once seemed so eminently presidential.

Think of it this way: American voters have for decades now sent their presidents to Washington in hopes of delivering some mortal blow to the status quo. Once in office, it’s hard for any president to fully embody the reform that a restive electorate may have hoped for. But it’s considerably easier if you can contrast yourself with an adversary who embodies the kind of outdated politics, ideological rigidity or divisiveness that repelled those voters in the first place.

And so President Ronald Reagan benefited immensely from his cordial back-and-forth with Speaker Thomas P. O’Neill Jr., who was the very picture of an old-time, cigar-chomping liberal pol. Bill Clinton regained his footing, after disastrous midterm elections in 1994, largely thanks to the contrast with Speaker Newt Gingrich, who came off as petulant and mean-spirited. (Gingrich, speaking to George Stephanopoulos of ABC on Tuesday, said he thought Palin needed to “slow down and be more careful and think through what she’s saying and how she’s saying it.”) Both presidents Reagan and Clinton portrayed themselves as standing between the public and a bunch of extremists in Congress.

George W. Bush, on the other hand, never really found his foil — and though he won re-election, he eventually paid the price. He and his allies tried at various times to elevate a Michael Moore or a Howard Dean, but none of these men really represented the mainstream of Democratic opposition, and by his second term Bush ended up looking more divisive than the congressional leaders who opposed him.

Sometime next year, when Republicans settle on a presidential candidate, Obama will have an adversary chosen for him. But for now, he could clearly do worse than to have Palin overshadow the party’s more predictable leaders in Congress. With every controversial tweet or video, Palin makes Obama, who has often struggled to project the regality of the office, seem more like the post-partisan grownup he always intended to be.

Shortly after Obama’s speech last week, his opponent from the 2008 campaign, Sen. John McCain of Arizona, issued a gracious statement thanking the president for his call for civility. Perhaps Obama wanted to thank McCain, as well — for having created the Sarah Palin phenomenon, thus giving the president’s words more resonance than they otherwise might have had.

© 2011 The New York Times Company