Updated: 1:16 p.m.

Sen. Lisa Murkowski’s potential primary loss in Alaska could be another Republican Senator’s gain, given it would set off a leadership race for a new vice chairman of the GOP Conference.

With unofficial results Wednesday morning showing Murkowski narrowly trailing her conservative, tea-party-backed challenger Joe Miller, it appeared the one-term Senator might become the third Senate incumbent to lose a primary this year.

If that happens, Senate GOP aides said, Sens. Tom Coburn (Okla.) and John Barrasso (Wyo.) could be candidates for Murkowski’s No. 5 leadership slot.

“Barrasso and Coburn have done a lot for the Conference; they would make a strong argument for vice chair,” one senior Senate GOP aide said. “If she loses, I imagine there will be a campaign for that leadership spot.”

Coburn and Barrasso were key figures in the GOP attempt to filibuster the Democrats’ health care reform bill last year. Coburn had been seen as a rabble-rouser, but in recent years, he has gained more credibility and respect within the Conference, another Senate GOP aide said.

Sen. Mike Johanns (Neb.) was also mentioned as a potential future leader. Chief Deputy Minority Whip Richard Burr (N.C.) is also well-positioned to run, but he must first survive his own tough re-election bid.

However, there also may be pressure to fill Murkowski’s spot with another woman, given that GOP leaders have tried to show diversity in their leadership team. But there are only three other female GOP Senators from which to choose.

Of the three, Sen. Susan Collins (Maine) would be the most likely candidate for a leadership post, but her centrist leanings and the moderate nature of her state may make toeing the party line as a leader tough for her. Several aides speculated that she might not be interested in the post.

Similarly, Sen. Olympia Snowe (Maine) is a centrist who is widely seen as uninterested in leadership, particularly because she is one of the most likely Republicans to vote with Democrats on social and spending issues. However, Snowe is a member of the vote-counting team for Minority Whip Jon Kyl (Ariz.).

Sen. Kay Bailey Hutchison (Texas) is likely out of the running for leadership because she is planning to retire in 2012 and already resigned a leadership post to run unsuccessfully for governor this year. She lost the primary to Gov. Rick Perry. However, Hutchison was recently appointed as an unofficial adviser to Minority Leader Mitch McConnell (Ky.).

Though public polls before Tuesday’s primary showed Murkowski with a healthy advantage, Miller leads the incumbent 51 percent to 49 percent, with 98 percent of precincts reporting. Final results may not be known for a week or more because, as the Anchorage Daily News reported, about 16,000 absentee ballots still need to be counted.

There was little sympathy for Murkowski’s predicament on Capitol Hill, however. Several aides said the Senator, who was originally appointed in 2002 by her father — then-Gov. Frank Murkowski (R) — did not take her challenger seriously enough, particularly in a year where anti-incumbent sentiment has been sweeping the country.

“Murkowski is a perfect example of an incumbent that loses in this environment. Everyone urged her to get on the air, define her opponent, run like you’re 20 points down, and she just wouldn’t do it,” the senior Senate GOP aide said.

The aide added that Sen. John McCain (R-Ariz.) trounced his primary opponent on Tuesday by running just such a campaign. “The contrast between McCain and Murkowski’s campaign tells you all you need to know about winning and losing this cycle,” the aide said.

Jessica Brady contributed to this report.