"What I have asked is for Alaskans to judge me on my performance," she said recently.
Murkowski touts her efforts to bring a natural gas pipeline to the state and to open the Arctic National Wildlife Refuge (search) for petroleum development as reasons to elect her to a full term.
She gets her chance to see how those accomplishments stand up to the nepotism issue in Tuesday's primary election against three Republican challengers.
Waiting to take on the winner is the likely Democratic candidate, former Gov. Tony Knowles (search).
Lisa Murkowski, 47, the front-runner, is a lifelong Alaskan, attorney and thrice-elected legislator who has never before run in a statewide election.
In 2002, her father gave up the U.S. Senate seat he held for 22 years to run for governor and the Alaska Legislature changed state law to allow the new governor and not the incumbent — Knowles — to fill Senate vacancies.
After winning the governor's office, Frank Murkowski conducted what he said was an exhaustive search for the Alaskan he said was the most qualified replacement, and unveiled a name that had been in no one's betting pool — state Rep. Lisa Murkowski.
Mainstream Republican leaders have embraced her. She's gotten the blessing of Alaska's senior senator, Ted Stevens, who called her "a hell of a lot better senator than her dad ever was."
She's been endorsed by President Bush and Vice President Dick Cheney, who made a campaign appearance in Anchorage. There has been a pipeline of Cabinet secretaries choosing Alaska to announce federal programs.
She supports tax cuts championed by President Bush and emphasizes her close relationship with Stevens and Rep. Don Young.
Money has poured in to her campaign since she began campaigning in January 2003 and she had raised $3.75 million through Aug. 4.
Her three Republicans challengers do not believe she's the best person for the job: Former state Senate President Mike Miller, 53, a gift shop owner from North Pole who spent 18 years in the Legislature; Wev Shea, 60, the former U.S. attorney for Alaska, now in private practice, and perennial candidate Jim Dore, an Anchorage house framer.
Miller has not been subtle in reminding voters of the circumstances of Sen. Murkowski's appointment. A mailer last week showed a frog with a gold crown under the headline "Kiss monarchy goodbye."
Miller's campaign also has been tagging Murkowski with a label considered leprous by Alaska Republicans: liberal.
Miller bills himself as a "trusted conservative."
Miller picked up endorsements from Lt. Gov. Loren Leman and former Anchorage Mayor Tom Fink. But he's raised a fraction of Murkowski's total, just $258,616 through Aug. 4, including $200,000 of his own money.
Shea's credentials — Naval flight officer who served in Vietnam, prosecutor, advocate of tough drug laws — are as conservative as Miller's, but he's been beating one drum: corruption in the state Republican Party.
Shea has criticized Murkowski and Miller — plus Stevens and the elder Murkowski — for continuing to embrace party Chairman Randy Ruedrich, who paid a $12,000 fine this year for violating state ethics law. Ruedrich admitted to three violations during his tenure as a $118,000-per-year member of the Alaska Oil and Gas Conservation Commission (search).
Lisa Murkowski said she would not make personal attacks and would focus on her record and vision.
"It's about articulating a vision for the state of Alaska — and going beyond articulating," she said at a recent luncheon.