ANCHORAGE  The message might have seemed gracious, on its face.

“Thank you for your service, Sen. Murkowski,” Sarah Palin wrote on her Twitter account on Tuesday night after Senator Lisa Murkowski conceded to Joe Miller, the political novice Ms. Palin had endorsed in Alaska’s Republican primary. Yet in the same message, Ms. Palin had reveled in Mr. Miller’s stunning upset, writing, “Do you believe in miracles?”

It took Sarah Palin just four years to help dismantle the political empire the Murkowski family took three decades to build.

In 2006, she ousted Gov. Frank H. Murkowski from the governor’s office, embarrassing him by 30 points in a Republican primary. But the strange tango of tension between Ms. Palin and Ms. Murkowski, two very different women who proved unable to share the small stage that is Alaskan politics, predated even that defeat.

“I don’t understand it,” said John Bitney, who was a top adviser to Ms. Palin during her run in 2006 and worked as campaign manager for Ms. Murkowski this year. “The back-and-forths have been all out in the open. I don’t know what drives them.”