Many Republican strategists have argued that it would be difficult for someone to run for governor in 2010 and turn around immediately, while running a state, and run for president in 2012. Gov. Tim Pawlenty of Minnesota announced last month that he would not seek re-election when his term expired in 2010, as he considers a race for president.

Quitting midterm, however, is highly unusual. It set off speculation about what led her to leave so abruptly. One interpretation among Republicans was that she had simply underscored how erratic she is as a politician.

“Good point guards don’t quit and walk off the floor if the going gets tough,” said John Weaver, a former senior strategist for Mr. McCain. “Today’s move falls further into the weirdness category; people don’t like a quitter.”

But some of her supporters argued that this could actually provide Ms. Palin an opportunity to recover from what has been a damaging year for her, and prepare herself for the 2012 race. She has been enmeshed in continuing battles with members of both parties in her Legislature.

The sheer distance of Alaska from the rest of the country complicated her ability to take care of the most basic kind of presidential preparation work: going to Republican Party dinners, developing a network of fund-raisers and supporters and becoming educated about the issues.

In addition, Ms. Palin just signed a lucrative contract to write a book.

“I think she is trying to determine how she can better get to where she’d like to be,” said Speaker Mike Chenault of the Alaska Legislature, a Republican from the Kenai Peninsula. “And she figures that if she resigns, people can’t be taking so many potshots at her.”

Image At a Friday news conference, Gov. Palin said, I am determined to take the right path for Alaska even though it is unconventional. Credit... Robert DeBerry/The Mat-Su Valley Frontiersman, via Associated Press

William Kristol, the editor of The Weekly Standard and a supporter of Ms. Palin, said that in the end, this could turn out to have been a smart move.