Alaska's Libertarian Party over the weekend closed the door on a potential run by Sen. Lisa Murkowski on its ballot line this November. 

Murkowski is still battling Tea Party-backed Joe Miller, who leads her by less than 2,000 votes in the state's Republican primary. Some 24,000 ballots must still be counted. But speculation about a third-party or independent run for Murkowski in November began almost immediately after last Tuesday's primary. 

The vice chairman of the state's Libertarian Party, Harley Brown, told The Hill that a supporter not affiliated with the Murkowski campaign reached out to the party and inquired about the possibility of a Libertarian run for Murkowski, should she end up losing to Miller in the primary.

"We started getting all sorts of calls and people were starting to speculate, so we just decided to put an end to it right away," said Brown. "We unanimously decided that it wouldn't happen." 

The vote was 5-0, according to Brown.