Sen. Lisa Murkowski (R-Alaska) will likely be forced out of her party leadership position should she decide to launch a write-in or third-party candidacy, a Senate Republican said Wednesday.

Murkowski, who conceded the GOP primary last month to Fairbanks lawyer Joe Miller, could announce as soon as Thursday whether she will continue her campaign for re-election as a write-in candidate. She has also held talks with the state’s Libertarian Party leaders about running under their flag.

Although Senate Minority Leader Mitch McConnell (Ky.) and other GOP leaders have not yet formally discussed what to do if Murkowski does run, the Senate Republican said there is likely no scenario in which she would be allowed to remain Republican Conference vice chairwoman.

According to this source, Murkowski could simply resign her position, or McConnell and other leaders could press her to resign. The conference could also formally vote to strip Murkowski of her leadership mantle.

Assuming she does stay in the race and is stripped of her title, Republicans would be forced to wait until after the November elections to vote to install a new member in her position.

Republicans, however, said they hope Murkowski drops the idea of continuing her re-election efforts. “She’s an adult. She lost the race,” one senior GOP Senate aide said.

Even as Murkowski has flirted with the possibility of continuing to campaign, Republicans have quickly fallen behind Miller, who upset Murkowski thanks to the support of members of the tea party movement.

For instance, McConnell has contributed $5,000 to Miller’s campaign through his Bluegrass political action committee, while the National Republican Senatorial Committee has donated $42,600.

Murkowski was traveling in rural Alaska and could not immediately be reached for comment.