Senate candidate leads with her gut

(CNN) - A defiant Alaska senator was on the campaign trail this weekend.

Sen. Lisa Murkowski, who is facing a tough three-way race in the state, said her gut is telling her she's leading her opponents.

"My gut tells me we are winning this campaign and we are doing so in a big way," Murkowski told CNN's Drew Griffin on Saturday. "I'm feeling extraordinarily good about where we are right now."

Murkowski launched a write-in bid for Senate after she lost the GOP primary to Tea Party-backed Joe Miller earlier this year, and they will both face Democrat Scott McAdams in Tuesday's election.

When asked if she ever thought her career would come to a write-in candidacy given her famous Alaska last name, she said she "never really thought about it, no."

"If I had I probably would have taken my husband's name," she said.

But she acknowledged that the experience will make her a different kind of senator if she returns to Washington, and called the break from the GOP "really very liberating."

"I know very well who will have returned me to Washington, D.C., to the United States Senate," Murkowski said. "And it will be these people in this state and nobody else."

She skirted the issue when asked what party she would caucus with in the new Congress and said she would be returning to represent "Alaskans interest," instead of the Republican Party's.

When CNN caught up with Miller, he too sounded confident.

"I know the Alaska people are behind us solidly," Miller said. "I'm excited that we can feel the momentum."

Recent polls show Murkowski and Miller in a deadlocked race with McAdams trailing.

– CNN's Drew Griffin and Kathleen Johnston contributed to this report