But since being embarrassed in an upset by Mr. Miller, a protégé of Sarah Palin’s, in the Republican primary, Ms. Murkowski has defied conventional wisdom and her colleagues in the Republican establishment by waging a credible race as a write-in candidate. Analysts and Alaskans now say she could overcome the odds and logistical hurdles to win, something no senator has done since Strom Thurmond of South Carolina in 1954. Or she could be a spoiler.

Democrats insist that their nominee, Mr. McAdams, can pull out a victory in this heavily Republican state if he can paint Ms. Murkowski as too conservative, and her write-in campaign as too risky, for Democrats who might defect to her out of fear of a victory by Mr. Miller.

The night after the federation conference, it was Mr. Miller and Mr. McAdams who appeared together for a debate at the University of Alaska Fairbanks. Ms. Murkowski was nowhere to be found, but that did not stop the other two from attacking her: She is too liberal. No, she is too conservative.

“Maybe we ought to debate Lisa for the rest of the night,” Mr. McAdams quipped at one point. “‘What do you think, Joe?’”