Over the past several weeks, Republicans have watched squeamishly as presidential contender Rick Santorum has waded into multiple controversies that risk alienating half the 2012 electorate: women.

But in fact, Santorum has grown more popular among women while talking about his opposition to abortion, his disapproval of birth control and his view that the federal government shouldn’t pay for prenatal screenings. A new Washington Post-ABC News poll shows not only that Santorum is doing better among GOP women than he was a few weeks ago, but also that he is less unpopular — and also less well known — among Democratic and independent women than his Republican rivals Mitt Romney and Newt Gingrich.

Voters and political strategists alike say Santorum’s rise has less to do with his views on these issues than on his ability to relate to the daily struggles of the middle class.

Nonetheless, the former senator from Pennsylvania and the other Republican candidates remain largely untested by the dynamics of a general election in which independent and Democratic women are expected to play a deciding role.

All of the campaigns — and the White House — are paying close attention to this major voting bloc, exploring how women feel about hot-button social issues and economic matters. Santorum’s views on health issues do not appear to have hurt in the primary. Yet he and the other Republican candidates are acutely aware of the danger those issues could present this fall.

“I’m still on the fence, but it’s not looking good for the Republicans,” said Bonnie Diehl, 45, an independent voter from Rochester, N.Y., who owns a house-cleaning business. “They’re laughingstocks. I’m trying to pay a mortgage, and I’m a cleaning lady, so of course I took a hit because that’s the first thing people are going to let go. And they’re trying to fly their conservative, back-in-the-’50s flag. I mean, let’s face it: Nobody leads the ‘Leave it to Beaver’ life. It’s over.”

The Post-ABC poll, conducted on the heels of a week of scrutiny of Santorum’s conservative views on a variety of women’s health issues, shows that his popularity among GOP women has moved up 13 points since January, with the biggest bump in the past week, so that 57 percent hold a favorable view. Santorum is now within reach of Romney on that score: Sixty-one percent of Republican women view Romney favorably. Romney has higher negative ratings among GOP women than Santorum does — 28 percent to 18 percent — and those negative ratings of Romney have grown over time.

Romney may have an edge with Republican women in some of the upcoming contests: A new NBC News/Marist poll shows that he leads Santorum among women and men in Arizona, and that among GOP women, he holds 46 percent while Santorum has 23 percent.

But there is no evidence that Santorum’s position among women in either party has dropped in recent weeks. That is a surprise to some Republicans, who have watched uncomfortably as he has engaged in high-profile discussions about abortion, contraception and prenatal screening.

Much of the talk has centered around past speeches and interviews, in which Santorum declared that birth control doesn’t work and that it “is harmful to women” and the country. He argued that the use of birth control encourages sex outside of marriage, particularly among the young. On abortion, Santorum said that the government should not fund prenatal testing because in the majority of cases when such tests diagnose a disability in the fetus, women choose to abort.

“I’m not a believer in birth control, artificial birth control,” Santorum — who is Catholic and with his wife, Karen, has seven children — said in a 2006 television interview. “I think it goes down the line of being able to do whatever you want to do without the responsibility that comes with it.”

Many Republicans consider contraception a losing debate. Birth control pills were first approved for use in the United States in 1960 and more than 12 million American women use them, according to the Centers for Disease Control and Prevention.

The subject surfaced again during a Republican debate this week. Asked their views on the subject (and briefly booed by an audience that seemed to recognize the perils of the question), the candidates steered away from speaking directly to their positions. Instead, Santorum, Romney and Gingrich sought to characterize the issue as a question of religious freedom — and to accuse President Obama of attacking religious liberties by seeking to mandate that all employers, even religious institutes, cover contraceptives for employees.

“This isn’t an argument about contraceptives,” Romney said. “This is a discussion about, are we going to have a nation which preserves the foundation of the nation, which is the family, or are we not?”

Overall, Santorum’s — and the other Republicans’ — popularity among Democratic and independent women remains weak, according to the Post-ABC data, with Gingrich leading the pack with the highest negatives among both groups and Romney not far behind him. Santorum is viewed unfavorably by 40 percent of Democratic women and 36 percent of independent women; Romney by 55 percent of Democratic women and 43 percent of independent women; and Gingrich by 63 percent of Democratic women and 58 percent of independent women.

Santorum’s popularity has probably risen, several Republicans said, because he has stuck to his views while working to change the subject back to the core issue of the economy. That is something that Romney, despite his business background, has not done well, several Republican and Democratic strategists said.

“I just don’t think Romney knows what life out here in the middle class is like at all — or cares,” said Dorothy Theis, 78, a retiree from Corcoran, Minn., who caucused for Santorum this month. Santorum’s social views don’t hurt because they are believable, she added.

In an interview with Charlie Rose last week, Santorum distanced himself from the controversial remarks of a top political supporter, Foster Friess, who joked that when he was young, women prevented pregnancy by holding an aspirin between their knees. Santorum called the joke “stupid” and touted his own support for Title X, which provides poor women with birth control. He also tried to turn the conversation to manufacturing and energy, about which he had just given a speech in Detroit.

Santorum is the only candidate who talks regularly about his family — and even about the price of milk, as he did recently. His campaign, too, has taken pains to cast his policies in a woman-friendly light, issuing a policy statement that describes his mother as the “primary breadwinner” when he was growing up and his wife as a lawyer, nurse and author.

“Rick knows firsthand what it means to run the carpool, pick up the kids from practice, help with homework and drop them off at their friends’ houses, all while trying to get to work on time or home for dinner with the family,” the statement reads.

One Republican strategist who spoke on the condition of anonymity to speak freely said polling data and focus groups of women show that they are less turned off by candidates’ views on women’s health issues than they are by the bickering on the debate stage.

“What I find is that women tend to be remarkably practical in these conversations,” the strategist said. “How is this going to impact the daily lives of myself and my family, at the very practical level?”

That reality creates peril for Obama and Democrats, too — who have tried to frame the discussion about contraception as one that Republicans are driving, but who are doing a lot of the driving themselves.

Winning women’s votes is a key strategy for Obama as he seeks a second term in part because that part of the electorate was so crucial to his victory in 2008. The gender gap — the fact that more women voted for Obama than men — disappeared in the midterm elections of 2010, and Democrats widely agree that reclaiming it is vital to their success this year.

Obama has struggled to strike a balance between women and religious voters, most recently in December when his administration overruled an effort by the Food and Drug Administration to allow the morning-after pill to be sold to teenagers without a prescription. Obama seemed to be trying to reposition himself with women earlier this month when he rolled out a policy — which he later amended — requiring employers to cover the cost of contraception in their health-care policies.

As if to keep attention trained on Republicans and how they navigate these issues, the Obama campaign helped organize more than 1,000 house parties on Wednesday for women to come together to watch the presidential debate.

“No one is making birth control a topic,” Santorum’s longtime media consultant John Brabender told The Post earlier this week. “It’s not an agenda that anyone’s running on. But it’s a distortion that works to [the other side’s] benefit to imply we’re for limiting access to birth control.’’

The Post-ABC poll was conducted Feb. 15 to 19 among a random national sample of 1,012 adults. The margin of sampling error for the full poll is plus or minus 3.5 percentage points.

Polling analyst Scott Clement and polling manager Peyton M. Craighill contributed to this report.