Sarah Palin dropped a heavy hint Tuesday that she might seek to run for the White House in 2012 as champion of America's Republican right.

Speaking to ABC television's Barbara Walters, the former running mate in John McCain's failed 2008 presidential bid gave every appearance of releasing a trial balloon.

"That certainly isn't on my radar screen right now, but when you consider some of the ordinary-turning-into-extraordinary events that have happened in my life, I am not one to predict what will happen in a few years," she said.

She stated her desire was to "help our country." Then, asked if she would play a "major" role in the 2012 presidential election, she answered: "If the people will have me, I will."

Palin is at the start of a publicity blitz for her memoirs, "Going Rogue," which went on sale Tuesday with a huge initial print run by HarperCollins Publishers of 1.5 million copies.

But the book tour is only part of a wider push to promote the unlikely comeback of one of the most unusual and polarizing figures in US politics.

A poll this week showed just nine percent of voters would definitely back her in a presidential election.

Yet the public's fascination with Palin and soaring sales of her book show she has star power that much better established politicians struggle to match.

Her appearance Monday on the popular Oprah Winfrey talk show sparked frenzied media reaction, with big news organizations live blogging the show and hosting debates on her performance.

There's no doubting the fragility of Palin's CV.

She has a colorful, sometimes messy family life and she mystified many when she resigned this year as governor of Alaska.

Her performance alongside McCain in last year's battle against Barack Obama for the White House was patchy. An interview with CBS's Katie Couric in particular was a disaster.

She is the butt of jokes for television comedians, with late night host David Letterman's new running gag dubbed: "Things more fun than reading the Sarah Palin memoir."

Number 14 on his list? "Driving a Jeep into a tree."

Yet Palin also has fervent support as the unofficial voice of the most active Republican opposition to Obama -- the "tea party" protestors and others proclaiming what they consider to be core American values of small government and self-reliance.

She may be hated by Democrats, but her favorable rating among Republicans is a whopping 76 percent, according to the latest Washington Post/ABC News poll.

Palin seeks to portray her turbulent personal life -- not least the teen pregnancy of one of her daughters and the father's appearance in Playgirl -- as evidence that she shares ordinary people's problems.

She reinforced that image of the moose-hunting mother turned savior-of-the-nation in her appearance, alongside two of her daughters, in Tuesday's ABC interview with Barbara Walters.

Daughter Piper, aged eight, revealed that her mother makes excellent hotdogs with cheese -- from Alaskan moose -- while Willow, 15, gave her own little push to the Palin presidential bandwagon.

"That would be cool," Willow answered when asked if she wanted her mother to run.