By using his mighty megaphone for raunchy name calling, Rush Limbaugh has handed the Democrats a big fat gift.

Whatever the damage to the nation’s top radio talker, he has put a face on the argument that President Obama’s party has been mounting for months—that Republicans are waging a “war on women.” In calling Georgetown law student Sandra Fluke a “slut” and a “prostitute” merely because she testified to Congress in favor of insurance coverage for birth control, Limbaugh has given the Democrats an indelible image to make their case.

“I don’t know any woman in America who finds being called a ‘slut’ funny,” Debbie Wasserman Schultz, the Democratic national chairman, told me. She was referring to Limbaugh’s explanation that his attempt at humor had gone awry. “To suggest that in exchange for access to contraception a woman should have to post sex tapes is just so outrageous.”

The Florida congresswoman also took a shot at Mitt Romney for his tepid response to Limbaugh’s three-day assault on Fluke. “The most their frontrunner could bring himself to say is that he wouldn’t have chosen those words,” Wasserman Schultz says. “You have countless candidates quaking in their boots when asked to criticize him.”

A onetime Romney adviser didn’t argue the point. The former Massachusetts governor “didn’t help himself,” says Alex Castellanos, a top strategist for Romney’s 2008 presidential campaign. “He had an opportunity to demonstrate strength. He left the bat on his shoulders.” (Romney’s campaign declined to comment.)

But the Obama camp wasted no time in trying to score runs. Shortly after the president called Fluke to commiserate over Limbaugh’s attack, the White House announced he would deliver the commencement address at Barnard College, a prominent women’s school. House Minority Leader Nancy Pelosi jumped into the fray by calling Fluke on Monday.

With a few incendiary phrases, Limbaugh turned on its head a controversy that had badly burned the administration. Even Vice President Biden says the White House “screwed up” last month by insisting that Catholic organizations cover birth control in their health plans. Despite a subsequent compromise, the misstep allowed the Republican candidates to denounce the president for an assault on religious freedom.

“There are a lot of voters out there who view the Obama position on contraceptive coverage very unfavorably,” says Dan Schnur, a former John McCain adviser who now runs the politics institute at the University of Southern California. “But they don’t want to see a college student beaten up and called names for taking the other side.”

And if Limbaugh, a pillar of the conservative movement for two decades, is weakened by the uproar, so much the better for his liberal antagonists.

El Rushbo continued his damage-control campaign on Monday as more advertisers, including AOL, bailed on his syndicated program, bringing the total to nine. After apologizing to Fluke on his website on Saturday, Limbaugh told listeners on his radio program Monday that those on the left will “say or do anything” to advance their agenda. “But this is the mistake I made: in fighting them on this issue last week, I became like them. That was my error. I became like them. And I feel very badly about that.”

Limbaugh’s show is a huge moneymaker for the more than 600 stations that carry it. So far only one, Hawaii’s KPUA, has dropped him, with the parent company’s president saying Limbaugh had “crossed a line of decency.” Sometimes there is a wildfire effect, as Don Imus learned in 2007 when he lost his radio and cable outlets after calling the Rutgers women’s basketball team “nappy-headed hos.” (Imus, whose show is now carried on Fox Business Network, called Rush “a fat, gutless, pill-popping loser” who had issued a “lame apology” rather than visiting Fluke.) But toppling Limbaugh, who earns $50 million a year for his enormous reach, would be a different order of magnitude.

It’s one thing for Limbaugh to taunt Obama or to hurl one of his patented insults, “feminazis,” at an entire gender. But Fluke, a mild-mannered woman who has quietly fought back on such venues as the Today show and The View, has proved a telegenic victim.

Michael Harrison, editor of the industry magazine Talkers, says the uproar is overblown. While Limbaugh was “very smart to apologize,” says Harrison, he is “basically an entertainer” who has again drawn enormous attention to himself.

“Just as Rush Limbaugh beating up on Bill Clinton every day did not cause Bob Dole to win, his impact on politics is far less than the media would believe. I don’t believe people are going to blame Romney or Santorum based on the fact that a radio talk-show host called a woman a slut.”

Wasserman Schultz rejects this just-a-radio-guy formulation, saying Limbaugh’s “power over the Republican Party is immense.” She pointed to recent comments by longtime GOP strategist and Bush White House aide Mary Matalin, who told CNN: “The Republicans would not have ascended to the majority in 1994 without Rush Limbaugh. There wouldn’t be a moderate conservative movement without Rush Limbaugh. There would not be a voice for the flyover country in mainstream America without Rush, and there will be no victories in the fall without Rush.”

Castellanos echoed that judgment: “He is, I wouldn’t say the intellectual leader, but an intellectual leader of the Republican Party.” The larger problem, he says, is the way that Limbaugh’s comments reinforce a Democratic narrative about conservatives who oppose abortion. “We have just handed them the cudgel one more time, playing into the stereotype that Republicans are anti-women.” Matalin, for her part, blames “Democratic demagoguery” for distorting Limbaugh’s intent.

On the campaign trail, Rick Santorum, more comfortable in the conservative fold than Romney, went a step further, calling Limbaugh’s comments “absurd.” But, he added with a touch of dismissiveness, “an entertainer can be absurd.” Newt Gingrich tried to blame his favorite target, saying on Meet the Press that he is “astonished at the desperation of the elite media” for avoiding such issues as gas prices, the budget deficit, and unemployment, only to “suddenly decide that Rush Limbaugh is the great national crisis of the week.”

There is, of course, an element of selective outrage in such matters. Fluke’s first television interview was with MSNBC’s Ed Schultz, who was suspended last year—and had to apologize—after calling radio host Laura Ingraham a “right-wing slut.” Democrats mostly stayed quiet then, while Fox’s Sean Hannity denounced Schultz over the S word, insisting there are “certain words you never say about a woman, to a woman, ever, ever, ever.” This time, Hannity is defending Limbaugh.

The larger problem for Republicans dates to the aftermath of the 2010 elections, when the GOP used its new House majority to defund Planned Parenthood. The issue surfaced again when a failed Republican candidate from Georgia helped convince the Komen Foundation to cut off funding for Planned Parenthood, starting a firestorm that caused the breast-cancer group to reverse its decision. Limbaugh, says Democratic strategist Jenny Backus, “basically put the fudge and cherry on top of a sundae the Republicans had already made.”

Most Republicans I spoke with on Monday made no attempt to hide their disappointment at what Limbaugh had wrought. “It just prolongs a debate about contraception, and we don’t win that debate. Rush keeps the story going,” says former Virginia congressman Tom Davis.

GOP strategist Leslie Sanchez was more optimistic that the debate would evolve into one over government intrusion in Catholic institutions. “The Republicans have mismanaged the messaging on this issue,” she says. “It’s a different question as to whether it turns off women eight months from now.”

That depends, in part, on whether Limbaugh can rally his dittoheads and put the controversy behind him.