Since resigning the governorship of Alaska, Sarah Palin has not disappeared from the public domain. Her autobiography sold more than two million copies in 2009. Her second book reached number two on the New York Times bestseller list in its second week. She provides political commentary on Fox News and has hosted her own reality show, Sarah Palin's Alaska. Palin is also seen as a darling of the Tea Party movement, several of whose members she endorsed in the recent midterm elections.

But despite her visibility, there are big questions about how much power Palin holds – and whether she has any chance of securing the Republican nomination to run against Barack Obama in 2012. So is it time for the Democrats to stop invoking her as a hate figure? Is the left giving her more coverage – and therefore credibility – than she really deserves?

Several journalists, including CNN's Gloria Berger, have spoken of "Palin fatigue". On the American news programme Morning Joe, the presenter Mika Brzezinski pointed out: "I don't want to overemphasise her news value . . . I mean, OK, you ran for vice-president, it was a huge failure. At what point do you not become news? At what point do we just ignore?"

So, as the Washington Post's Dana Milbank begins a month-long Palin moratorium and urges fellow journalists to stand with him, when should the media stop trailing Palin to every book signing/town-hall meeting/Tea Party conference, or dissecting every new tweet and Facebook post?

Not yet, I think.

In November last year the former Alaskan governor announced in an interview with New York Times Magazine that she was considering running for the presidency, and to that end "was having that discussion with her family".

Following that, a poll by Ramussen detailing the views of 1,000 likely Republican primary voters in the 2012 presidential elections placed Ms Palin, with 19 per cent of the vote, second only to the former Massachusetts governor Mitt Romney.

Then again, Palin trailed in fourth in a straw poll of the Republican state committee in the "kingmaker state" of New Hampshire. She was behind not only Romney, the serious contender, but also the Texas congressman Ron Paul and the former Minnesota governor Tim Pawlenty.

That straw poll listed 21 possible Republican nominees, perhaps highlighting the continuing uncertainty surrounding the GOP nomination. The Washington Post, however, sees the results as an indication that even with the rise of Tea Party, the party machine is likely to back an establishment candidate in 2012.

According to a recent Gallup poll of Republicans and Republican-leaning independents, Ms Palin has a net favourable rating of 22 per cent. Those who placed higher than her in the New Hampshire straw poll – Romney, Paul and Pawlenty – scored 23, 18 and 13 per cent respectively. Interestingly, Palin's fellow Fox News pundit Mick Huckabee, who came 12th in the New Hampshire poll, had the highest net favourability rating of 30 per cent.

Judging by these early indicators, the Republican ticket remains very much unwritten. There is a marked absence of any declared runner providing a rallying point for Republican attention, or the attention of the wider press.

The Gallup poll found that Palin was the most recognisable Republican, which if nothing else demonstrates her capacity to grab the attention of potential primary voters more successfully than her Republican competitors.

Her recognition rating of 95 per cent was 11 points ahead of Romney's. It remains important that those on the left maintain their focus, however fatiguing, on the obviously frenetic Ms Palin.