All of the Republican presidential candidates not named Mitt Romney have been trying desperately to make the case that they can beat President Obama this fall, hoping to blunt Romney’s electability argument that he is the only one in the race who can do that.

But on Thursday, in town hall meetings and other campaign stops across New Hampshire, where Romney leads by double-digit margins in most polls, the “not-Romneys” kept getting distracted by the urge to turn on one another.

Newt Gingrich, acknowledging that the Granite State is Romney country, attacked the current front-runner as a Massachusetts moderate, but he saved his sharpest criticism for Rep. Ron Paul (Tex.), whose supporters showed up outside a Gingrich event here with a poster of a famous New York tabloid cover depicting Gingrich, clad in diapers and wielding a rattle, as a crybaby.

On the airwaves, Paul, who will hold his first post-Iowa-caucus events here Friday, attacked Romney and Gingrich as being too close to Washington.

And Rick Santorum, fresh off a near-win in Iowa, pushed back against Gingrich, who dismissed the former senator from Pennsylvania as a “junior partner” during their time in Congress.

Santorum also forcefully tried to strip Gingrich of some of the credit for the 1994 Republican Revolution, which made Gingrich speaker of the House and is central to his claim that he is the truest conservative in the field.

“He sat on the sideline when I was out there putting my face and putting my reputation out to try to reform Congress,” Santorum told reporters in Northfield. “I think that tells you who’s got the courage to stand up and fight.”

Former Utah governor Jon Huntsman, who has lagged in the polls but devoted intense energy to New Hampshire, got a boost Thursday when he won the endorsement of the Boston Globe, Romney’s home-state newspaper.

But with a single weekend of campaigning left before Tuesday’s primary, with 23 delegates up for grabs, most candidates seemed split on whom to take the fight to — and unsure as to how to make their lines stick.

Beyond that, their messages and their reasons for running are coming across as muddled to some voters, who have been bombarded with ads and mailings.

Santorum, who added $2 million to his campaign war chest in the two days since his surprise second-place finish in Iowa, faced boos at a stop in Durham as he answered questions about his position on same-sex marriage. He is a longtime opponent of gay rights, which makes him popular with many conservative voters.

But while speaking at New England College, he was challenged on his position.

Santorum, who is accustomed to questioning from students and seems to somewhat relish it, first tried arguing that there is no compelling reason to change the laws banning same-sex marriage.

“Don’t you have to make a positive argument that the law should be changed?” he asked the crowd. “You, the person who wants to do this, tell me, what is the justification? What is the public purpose?” The event ended in boos for the candidate.

Catapulted to the top tier of the race by his Iowa showing, San­torum has attracted fire from the GOP establishment in the form of Sen. John McCain (Ariz.), the party’s 2008 nominee, and a top Romney surrogate.

“I respect Senator Santorum,” McCain said Thursday morning on CNN. “He and I had very strong differences on earmarking and pork-barrel spending. I believe that earmarking is the gateway to corruption. Senator Santorum supported it and engaged in it as much as he possibly could. “

Romney spent part of his day courting conservatives in South Carolina and didn’t attack anyone except Obama, picking up tea party lingo and calling him a “crony capitalist” for the president’s “recess” appointments to the National Labor Relations Board. The president and the GOP have been embroiled in a fight over the NLRB’s regulatory powers, and he decided to bypass Senate opposition Wednesday by appointing three members whose nominations had been blocked in the upper chamber.

Gingrich also called the appointments illegal.

At his stops Thursday, Gingrich faced tepid but interested crowds.

As he came and went, people gave him advice, sometimes conflicting: Hit Mitt; stay on the high road; talk more about taxes.

“I know a lot about your personal life, I know a lot about Freddie and Fannie . . . but it’s interesting to hear the ideas that you have put forth,” said Sam Greenlaw, 71, a retired small-business owner who heard Gingrich speak at the Littleton Opera House. “Those thoughts aren’t out there to the American. . . . We don’t know those things.”

Gingrich, whose wife, Callista, stood by his side as he spoke, seemed not to have a real answer: “Sometimes the nature of American news media and the nature of campaigning . . . [means] you are doing it through clutter,” he said.

Gingrich would not comment on any concerted effort among conservatives to defeat Romney. The one thing they agree on, he said, was that Romney was the least conservative candidate in the race. “We all have a common value system that is dramatically more conservative than Romney’s,” he said. “We are also competing with each other.”

Staff writers Rosalind S. Helderman, Sandhya Somashekhar and Philip Rucker in New Hampshire contributed to this report.