New Hampshire Republican operatives, already navigating recruitment calls from prospective 2012 presidential candidates, say they’re getting mixed messages about Sen. John Thune’s intentions.

The South Dakota Republican is one of Capitol Hill’s favorite rumored contenders. In the state that will host the nation’s first presidential primary, however, Thune has been slow to prove he’s serious about a White House bid.

He was in touch with Granite State political players regularly in the first half of 2009, but the calls dried up months ago.

“I haven’t heard from him since August. Nobody’s heard from him since then,” said one prominent GOP strategist who has yet to commit to a 2012 campaign but played a leading role in New Hampshire’s 2000 and 2008 GOP primaries. “I would love to work for him, but I’m convinced he’s not running.”

Granite State Republicans acknowledge that the 2012 cycle is beginning far more slowly than those of recent years. But some candidates are quietly more active than others. Days before the November midterms, Minnesota Gov. Tim Pawlenty temporarily shipped several staffers north to help the New Hampshire GOP, while promoting his political action committee Freedom First.

Pawlenty is the only prospective candidate with a staffer on the ground today, but former Massachusetts Gov. Mitt Romney is actively securing support from what remained of his 2008 presidential bid, when he finished second in the Granite State. Rick Santorum and Newt Gingrich have visited multiple times. Thune’s efforts may be limited to date, but he has at least one well-connected friend on the ground making calls on his behalf.

The Hanover, N.H.-based Gregory Slayton, a former Thune finance director and Bermuda ambassador under the Bush and Obama administrations, told Roll Call that he’s been “talking to friends and getting their input” about a potential Thune candidacy.

“There are a couple folks who appear [as if] they’re going to enter the race. Until the field gets a little clearer, it’s hard to say who’s the frontrunner. But I think John Thune would play very, very well in New Hampshire,” Slayton said, noting Thune’s friendship with Arizona Sen. John McCain, who is among the Granite State’s most popular Republicans. “Thune backed McCain very early in his presidential bid.” Roll Call reported this month that Thune has been seeking advice from McCain and other Senate colleagues about a White House bid.

Thune may be poised to use a geographic advantage to emerge from the Iowa caucuses with momentum heading into New Hampshire. South Dakota and Iowa, of course, share a border. They also share a major media market, meaning that Thune could be known to Iowa voters almost as well as those in his home state. President Barack Obama, then a Senator from Illinois, used a similar strategy in 2007 and 2008 to make frequent visits to Iowa.

It’s clear that the South Dakota Senator has work to do in New England, however, should he decide to run. He is virtually unknown among New Hampshire’s electorate, evidenced by his last-place finish in a late October poll. Just 1 percent of Granite State Republicans supported Thune in the survey by Public Policy Polling.

He raised some eyebrows by agreeing to a radio interview with a Concord, N.H.-based station last week, an appearance widely reported in Washington as evidence of a likely candidacy, but one that baffled local Republican strategists.

“It’s a tiny, tiny station. Anyone who’s serious about running, there’s usually a rhyme or reason, and wouldn’t do something like that,” said another local Republican operative who hasn’t yet committed to a 2012 campaign.

During the WKXL interview, which spanned several minutes, Thune said his team is “taking a hard look” at a potential presidential run. Thune’s former campaign manager, Justin Brasell, explained Thune’s decision to grant his first extensive local radio interview with the little-known station that has one of the smallest audiences in the Granite State. Brasell said it was a matter of timing, and that the station had reached out several months ago to see whether Thune could call in for an interview.

“We didn’t do anything to promote it. It’s a reflection I think of the hunger in the press for news about 2012,” Brasell told Roll Call. “It’s not a reflection of what the campaign is doing and where Sen. Thune’s organization is. … We finally got a time that had 10 minutes and he called in.”

Brasell did little to dispel the notion that his former boss will run for president. He said Thune “is highly likely to visit” New Hampshire and Iowa “after the first of the year.”

But it is Brasell’s shifting role that also has produced skepticism among some New Hampshire Republicans.

Having essentially served as Thune’s top political aide through the midterms, Brasell is opening his own consulting firm in Mississippi in the coming weeks. He was Thune’s campaign manager through the 2010 cycle — the Senator ran for re-election unopposed — and served as the lead staffer at his Heartland Values PAC.

“This move is not about John Thune. It’s about getting my kids who are now 5 and 3 settled into a house and putting roots in Jackson,” Brasell said. “I’m going to travel as needed. If Sen. Thune runs, decides to do that, I fully expect to be invited to participate and will relish that role.”

“He’s got a lot of smart people encouraging him to run and who would be helpful if he does,” Brasell continued. “I think some of my friends in New Hampshire might be misreading the tea leaves as to what my departure means.”