The Anchorage Daily News reports:

Murkowski wouldn’t discuss whether she’d pursue a third-party or independent write-in candidacy for the seat if she loses the Republican primary.

“It is way, way, way too premature to even be talking about that,” Murkowski said.

But a third party-run would be tough:

Alaska Division of Elections Director Gail Fenumiai told me it's too late for Murkowski to file to have her name appear on the ballot as an independent, so that would need to be a write-in effort. There is a Libertarian candidate in the race, Frederick Haase, who could choose to step down. The Libertarian Party could then select a replacement for him on the ballot.

There is no other third party candidate in the U.S. Senate race, so Libertarian would be the only option for Murkowski to join a new party for a run.

Of course, there are still 8,000 absentee ballots to be counted; Murkowski would need more than 60 percent* of them to overtake Miller. UVA's Larry Sabato says that "solid Alaska sources" say they "do not think there is any realistic chance Lisa Murkowski can make up the votes she needs."
From Larry Sabato, Clarification: Yes those 8000 outstanding ballots are not just R ballots, but a mix of both D and R, so let's say, tops, 6000 are R's. She'd have to win 4000-2000, or 2:1, to pick up 2000 votes from the absentees.
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