Republican Jon Huntsman met last week with Sen. John Thune (R-S.D.) and other Members, looking to build support on Capitol Hill in preparation for a likely 2012 White House bid.

Huntsman, who served as President Barack Obama’s ambassador to China until resigning April 30, made what Thune described as a courtesy call while traveling to key states on the Republican presidential primary calendar.

Thune told Roll Call that his relationship with Huntsman dates back to their mutual support for the 2008 presidential campaign of Sen. John McCain (R-Ariz.), adding that they have traveled together to Iraq.

“He’s just returned from a stint in China and is giving a lot of consideration whether or not to make this race, and I’m guessing he’ll probably say something before too long,” Thune said.

Huntsman, the former governor of Utah, is relatively unknown in Congress. But Senate Republicans seemed open to learning more about him, even though he would be running to unseat the administration in which he recently served in such a high-profile post.

“He’s going to have to make his case, obviously, to Republican primary voters if he decides to run. I don’t know that that’s a certainty yet,” Thune said. “But he’s obviously a very smart and very accomplished governor. He would enter the race at a time when I think people are looking for people who have solved problems. That’s why I think governors are making a very strong argument to the American people.”

Thune, the Senate Republican Policy Committee chairman and No. 4 in leadership, opted against a presidential bid earlier this year. He has not, however, ruled out running in the future or joining a ticket as the vice presidential nominee.

Member endorsements often have nominal traction with primary voters. But such support can translate into the grass-roots and fundraising support that is crucial to building a successful campaign operation. Huntsman spokesman Tim Miller said his boss is pleased with the reception he has received from Members since leaving Beijing.

“Gov. Huntsman has been very encouraged by all the positive feedback he’s received on the Hill in the short time he’s been back,” Miller said.

Since returning from China, Huntsman delivered a commencement speech in the early primary state of South Carolina and plans to head to New Hampshire later this month for a five-day Granite State blitz. The Republican unveiled a new federal political action committee within days of what had been a long-announced resignation as ambassador and has more campaign-style appearances before potential GOP primary voters planned.

The Huntsman camp, which continues to hire staff for a potential bid, has signaled he would make winning New Hampshire central to his primary campaign strategy. Sen. Kelly Ayotte, who has yet to meet or be in contact with Huntsman, said it is unclear whether the ex-ambassador can be successful there. The New Hampshire Republican said Huntsman’s prospects would be determined through extensive grass-roots campaigning and how he addresses his service to Obama.

“I don’t know how the people in New Hampshire will take him,” Ayotte said. “I do think, though, that one of the questions Republicans want to know is, certainly he’s worked with the administration. How does he feel that he’ll be in a position to beat the president given that he served underneath him? And, I think that’s an important question he’s got to get out and talk to Republicans about, and answer.”

Huntsman’s reception among Utah Republicans was mixed during his roughly one-and-a-half terms as governor. The charismatic chief executive was among Utah’s most popular governors ever, winning re-election in a landslide. He presided over a strong state economy, promoting and enacting unabashedly conservative fiscal policies. But some conservatives and tea party activists grew disenchanted with him during his second term, charging that he was too moderate on environmental and social policies.

Sen. Jim DeMint, who plans to be active in the GOP presidential primary after he settles on a candidate, said he has yet to meet Huntsman and doesn’t know much about him. But the South Carolina Republican, who regularly takes sides in GOP Senate primaries against the candidate perceived as moderate, or at least less conservative, said he looks forward to meeting Huntsman and learning more about him.

“A few people who know him have mentioned things to me. But I’m just going to wait and meet him myself and see what kind of candidate he is,” said DeMint, who in the 2008 GOP primary backed former Massachusetts Gov. Mitt Romney. Huntsman and Romney are both Mormons.

Senate Republican Conference Chairman Lamar Alexander said that Huntsman’s service in the Obama administration should not preclude him from running for president in 2012, although he made clear that it would ultimately be GOP primary voters who determine that. Alexander, the former governor of Tennessee, was a Republican presidential primary candidate in the 1996 race. The two have not met to discuss 2012.

“He’s perfectly well-qualified to compete for the presidency. He has a distinguished background as a governor and an ambassador. Primary voters can sort that out,” Alexander said. “But he’s certainly well-qualified.”