Buffing or besmirching the Palin aura is a risky business, people in both parties said.

Many Alaskans affiliated with the Tea Party still revere her, which makes it tricky for Republican supporters of the Parnell plan to speak too harshly. But she also evokes strong negative feelings across party lines in Alaska, Democrats say, partly because of her attack dog role during the 2008 presidential campaign and partly because of her decision to resign as governor, which many residents took as a slap. That makes the repeal forces hesitant to ask her to help or endorse their efforts — even if she had an inclination to do so.

“She did the right thing. She put in a tax that was tough on the big guys,” said Jack Roderick, 87, a major public figure since Alaska’s early statehood as a lawyer, author, former Democratic mayor of Anchorage Borough — and now leader of the repeal drive. But her image now is so divisive, he said, that active campaigning on her part would “probably not be helpful.”

Another former Anchorage mayor, Rick Mystrom, a Republican who is a co-chairman of a group called Vote No on 1, which is fighting the referendum, said a discussion of the Palin legacy would probably not factor in at all. “I don’t think we’re even going to touch on Sarah Palin, we believe that our arguments are so logical and rational,” he said.

Ms. Palin, who has been on a book tour and making political endorsements, did not respond to requests for comment.

Both parties are divided over how to tax the oil that shapes Alaska’s economic life. Mr. Parnell’s plan gained final approval in the State Senate by an 11-to-9 vote this past spring, with 11 Republicans voting yes, and two Republicans joining with the seven minority Democrats in voting no. Some prominent Democrats, meanwhile, including two former governors, Tony Knowles and Bill Sheffield, are supporting Mr. Parnell.

What complicates the picture for Mr. Parnell is that his new system will hurt state tax collections. Even he and his supporters say billions of dollars of tax revenue will be forgone in the early going, though they say that new drilling and production incentives will eventually build state revenues. The old law, called ACES, for Alaska’s Clear and Equitable Share, included an escalator clause that raised oil tax rates as profits went up; the new law scraps that for a flat rate.