Sen. John Barrasso (Wyo.) has the endorsement of conservative stalwart Sen. Tom Coburn (Okla.) to become the next vice chairman of the Senate Republican Conference — and that might be the crucial vote he needs to secure the post.

Barrasso on Tuesday declined to discuss his plans to succeed Sen. Lisa Murkowski (Alaska) as vice chairman, saying he was focused on doing his job as a Senator and helping to elect more Republicans on Nov. 2. But sources have confirmed Barrasso’s interest, and at least one GOP Senator noted that the first-term Republican has reached out to him in recent days to gauge support for his candidacy.

“He does have my support. I endorsed him,” said Coburn, who has enormous credibility with conservatives both on Capitol Hill and among GOP activists. “We’ve worked together a lot. He’s a real hard-core conservative, and if the position is open, I’m going to support him.”

Barrasso and Coburn, both physicians, have worked closely on health care reform over the past two years and helped lead the Republican opposition to the new law. Barrasso’s work on health care has endeared him to many of his GOP colleagues, and his conservative voting record has positioned him to earn the support of his colleagues for the vice chairmanship once he formally throws his hat into the ring.

The leadership election will occur after November general elections.

The position is open because Murkowski lost her August primary to Fairbanks attorney Joe Miller. Even if she were to stay in the race as a write-in candidate, many Senate Republicans likely would demand that she step down from leadership given her refusal to accept the will of GOP primary voters in her state — and support a challenger if she did not.

Senate Republican leaders have been reluctant to broach the subject of Murkowski’s successor in leadership, preferring to wait for her decision on her future and hoping that she bows out gracefully, saving them from dealing with her ouster. Still, Republican Conference Chairman Lamar Alexander suggested that Barrasso would make a solid addition to the leadership team should a vacancy occur.

[IMGCAP(1)]”I’m a big fan of John Barrasso,” the Tennessean said. “He’s arrived in the Senate with a lot of spunk and a lot of intelligence. He works hard, he knows the issues and he’s an excellent Senator.”

“I think it’s a little early to be making a judgment” about Murkowski’s successor, Alexander added. “That will be decided in November. But he surely is an excellent candidate. He’s widely respected in our caucus, and I have great respect for him and could work easily with him.”

Republican Senators-elect will participate in the next leadership elections. With the possibility that the 2011 freshman class could include a cadre of aggressive conservatives, Barrasso or another similarly right-of-center Senator might have an advantage in the race for vice chairman. But Coburn’s early endorsement of Barrasso likely would thwart any serious challenge from Barrasso’s right flank.

Barrasso remains tight-lipped on the matter, repeatedly side-stepping questions when asked to comment Tuesday. “I’m focused on getting more Republicans elected to the Senate, that’s what I’m focused on right now,” he said.

Murkowski, who missed votes Monday and Tuesday but was due back in Washington, D.C., today, has yet to announce her plans. Republican leaders have moved swiftly to back Miller in Alaska’s general election and worry that if Murkowski remains in the race she could split the Republican vote and push Sitka Mayor Scott McAdams (D) to an otherwise unlikely victory.

With Murkowski out, Republican operatives who follow the Senate see Barrasso and Sen. Mike Johanns (Neb.) as the leading candidates for vice chairman, the fifth-ranking of five leadership positions. The chairmanship of the National Republican Senatorial Committee is not considered part of the caucus leadership, and even the vice chairmanship is not seen as particularly powerful or influential.

However, Johanns announced last week that he would not seek the post. In a brief interview Tuesday, the Nebraskan explained that he did not wish to pursue leadership at this point. Johanns, noting that Barrasso called him to discuss the vice chairmanship, said he would make a decision about whom to support for the position following the midterm elections.

“To be very candid, I’m just not interested in that,” Johanns said when asked why he pulled out of the running. “Conference leadership sends you in kind of a different sort of direction. I like what I’m doing. … There would have to be a complete change in my interest toward it, because I’m just not interested in that.”

Coburn, who was also mentioned as a possible candidate for the vice chairmanship given his popularity with conservatives and good working relationship with Senate Minority Leader Mitch McConnell (R-Ky.), also said he preferred to work outside the leadership structure.

“I gave zero thought to it because there’s two types of leadership,” Coburn said. “There’s elected leadership and then there’s leadership outside of it, and we’ll have just as much power outside of leadership as we will in.”