NORTHFIELD, N.H.—Rick Santorum and Elsie Shute seem to be worried about the same elephant in the room this week.

Shute, a retiree,  came to hear the candidate after his good showing in Iowa—but she’s not convinced he’s the right guy to beat President Obama. “That’s my No. 1 criteria in deciding whom I’ll vote for,” she says of Tuesday’s primary here. “We’ve got to get Obama out of there.”

Santorum is so conscious that voters are assessing his electability —in New Hampshire as well as nationally—that he raises it at every stop. “I’m the only one in the field who ran as conservative in a Democratic state and won,” the former Pennsylvania senator said following a town-hall-style meeting at Merrimack Valley Railroad. “Mitt Romney hasn’t done that.”

During his first post-Iowa event this week, he was particularly pointed, exhorting the 200 potential voters who packed a senior center not to “buy the media hype.”

“Don’t buy the lie that you have to be a moderate to be able to win the election,” he said. “Had New Hampshire settled for George H.W. Bush, Ronald Reagan would never had been president. Bush won Iowa but Reagan won New Hampshire, and it made all the difference for this country.”

Animated and energized by his virtual tie with Romney in Iowa, Santorum is working hard to make the sale but the fact is, he is not a natural fit for a state that is socially liberal, but fiscally conservative.

On Thursday, he was booed at an event with college students when he was pressed on the subject of same-sex marriage and compared it to the illegality of polygamy.

Beyond  New Hampshire,  Republicans worry that  in a general election, his ultra-conservative positions on social issues could alienate the more moderate  swing voters and independents that play a huge role.

Even with his momentum from Iowa, he has an uphill climb: Mitt Romney has a commanding lead  in the state according to the most recent Suffolk University/7 News tracking poll in New Hampshire favored by 40 percent of likely voters, followed by Ron Paul (18 percent). Santorum sprung into third place after Iowa, but he’s still the choice of only 11 percent of likely voters. Fifteen percent remain undecided.

Still, Santorum has been looking for common ground, and voters are turning out in droves to see him. He has been zipping around the state like a rock star, holding marathon town-hall meetings and signing autographs. He takes questions for well over an hour but generally only gets to a few because he tends to be long-winded,  and  segues into other topics along the way.

He spends his time assailing big government as akin to Big Brother depriving people of their rights—a theme that plays well here. He vows to repeal the new health-care law in one of his first acts as president, and excoriates government regulations that he says strangle businesses.

But what he conspicuously doesn’t talk about are the social issues, which were the core of his Iowa campaign. He is anti-abortion, against gay marriage and highly critical of gays serving openly in the military.

A number of  voters said they decided to take a fresh look at him after his showing in Iowa. “He worked hard and I thought he deserved a chance to be heard,” said Diana Modugno, a retired federal-court reporter. “He’s someone who I don’t think would lie to us.”

Elsie Shute said she might be able to overlook his anti-abortion stand if she were convinced he could beat Obama. Patricia Jorgensen, a homemaker who supports abortion rights, said she might be willing to put aside Santorum’s anti-abortion views because she agrees with many of his other positions. “He says he’s going to go after entitlements and I’m for that,” she says.  “But I’m very undecided—torn between him and Romney—who can best beat Obama. I want to see if this guy has what it takes.”

Voters in New Hampshire historically make their decisions late, and intensely scrutinize candidates. Most say in polls that they vote solely on issues, but there is evidence that electability plays a significant role.

“Electability is ultimately what voters look at—they want to feel their candidate can beat the other guy,” says Andy Smith, the director of the University of New Hampshire Survey Center. “The calculation is to pick the most electable candidate that is closest to your political views.”

Thomas Rath, a Romney adviser and longtime GOP activist, surmises that electability may be particularly relevant in this cycle because the “overarching unifying characteristic of GOP primary voters is a shared desire to defeat Barack Obama.

“New Hampshire voters want to believe that their choice can not just be the nominee but can win the general election,” Rath says. “To win here, a presidential candidate must mix ideology with electability.”

Santorum will need to show that Iowa wasn’t a fluke, and to that end he needs to show he can cut it in New Hampshire. “Don’t pay attention to polls,” he told people Thursday. “And don’t defer your judgment to pundits... to people who don’t know any more about this race that you do. Trust yourself