WHEN Sarah Palin’s teenage daughter, Bristol, gave birth last month to the governor of Alaska’s first grandchild, America’s comedians had a field day. What would the new baby be called, given the Palin family’s unrivalled record for unorthodox Christian names? Palin’s other children are named Track, Trig, Piper and Willow.

Suggestions for the new arrival ranged from Takeetna - after a small Alaskan town up the road from the Palins’ home in Wasilla - to more fanciful concoctions such as Rifle Fanbelt and Tackle Musher.

One blogger suggested Trip, as a jocular reference to the arrest on drug charges a few days earlier of Sherry Johnston, the mother of Bristol’s boyfriend, Levi, the 18-year-old father of the child. Jaws dropped when the family announced that the infant boy would be known as Tripp Easton Mitchell Johnston.

Two months after she crashed to defeat as John McCain’s accident-prone side-kick in the 2008 presidential race, Palin remains a prime source of national hilarity. Yet the “hockey mom” who cracked jokes about pitbulls and lipstick and focused world attention on Wasilla enters 2009 as a key figure in Republican plans for political revival.

Palin ended 2008 with a striking run of personal successes in high-profile popularity polls. According to a poll by Gallup she was the second most admired woman of the year, after Hillary Clinton. Time magazine chose her as the world’s fourth most influential person, behind Barack Obama, Henry Paulson of the US Treasury and President Nicolas Sarkozy of France.

Last week she triumphed in an annual poll, commissioned by a property website, as the person Americans would most like to have as their neighbour. She finished ahead of Oprah Winfrey, the television chat show queen, and Michael Phelps, the Olympic swimmer.

For all the abuse she endured as an underprepared vice-presidential candidate who knew more about skinning moose than resolving Middle Eastern conflict, Palin continues to excite Republican voters enthralled by what they see as a unique political style that could one day put paid to Obama. She has not returned to the Alaska governor’s office to lick her wounds.

An internet campaign is already under way to promote Palin as the Republican party’s best choice to challenge Obama in the presidential elections of 2012. More than 60,000 people have joined TeamSarah.org, an umbrella group that unites numerous pro-Palin fan clubs such as Catholics for Sarah, Texans for Palin and Small Business-Owners for Sarah.

James Brislin, a Connecticut team member, noted that “the Republican party has lost its way . . . Sarah Palin is who we need moving forward”.

The 44-year-old governor is already facing conflicting pressures to map out a strategy that would give her a bigger voice in national affairs without alienating Alaskan voters, some of whom are already complaining that Palin has “not been paying attention” to the state’s mounting problems.

“Palin’s mindset is still all about the campaign rhetoric and her national aspirations,” said Andrew Halcro, a former rival turned Anchorage radio chat show host. “She has no clue what is going on in her own administration.”

Even before election day last November there had been feverish speculation in Anchorage that Palin was considering a run for the US Senate seat that was then likely to be vacated by Ted Stevens. He had been convicted last year on charges of corruption and faces a possible jail sentence.

Such a move would have brought Palin to Washington this year, where Republican heavyweights would have had plenty of time to strengthen her grasp of both domestic and international issues. The plan collapsed when Stevens refused to resign, ran again for reelection and was beaten by Mark Begich, the Democratic mayor of Anchorage.

Palin supporters promptly set their sights on Alaska’s other senatorial seat, currently held by Lisa Murkowski, the governor’s Republican colleague. There has been bad blood between the Palins and the Murkowskis ever since Frank, Lisa’s father, gave up his previous job as senator to become Palin’s predecessor as governor in 2002.

Alaska was outraged when Frank promptly exercised his powers as governor to appoint his daughter to the senatorial seat. Palin eventually profited from the nepotism row, challenging Murkowski Sr and ousting him as governor in 2006.

Some of her supporters believe she should now do the same to Lisa, keeping herself in the national spotlight and getting to Washington in 2010.

The Palin camp has since denied that it ever intended to challenge Murkowski and most analysts have concluded that it would be foolish for the governor to risk a bloody Senate battle if her real aim is to run for the White House two years later.

“If she were to kind of move me over. . . to run fornational office again,” said Lisa Murkowski, “I don’t know if Alaskans would look too favourably on that.”

The dilemma for Palin is that she needs a period of serious policy accomplishment to counter the relentless barrage of mockery that is shadowing her every move. One end-of-year award that Palin probably regrets went to Tina Fey, the late-night TV comedian who impersonated her.

In the widely reported list of the most memorable quotations of 2008, Fey was adjudged the winner for the line she used to mock Palin’s claim that Alaska’s proximity to Russia somehow made her an expert on Moscow. Fey-as-Palin joked: “I can see Russia from my house.”

Palin must now strike a delicate balance between dealing with the mundane chores of managing the state budget, which is heavily dependent on oil and gas revenues, and making herself part of the national debate on issues such as Gaza and Guantanamo, the very mention of which in a Palin context causes many Americans to giggle uncontrollably.

Last month Palin found herself addressing local complaints that she does not spend enough time in Juneau, America’s most remote state capital, and that she is happier to give interviews to People magazine than to the Alaskan press corps.

She hardly helped herself last week when, four days after her spokesman had declared that she would “not be issuing any statements” about Bristol’s baby, she issued a statement declaring herself “over the moon”.

She was also at pains to point out that Levi Johnston is not a high-school drop-out, as has been widely reported, but is pursuing an online high-school course while working as an apprentice electrician in the Alaskan oil fields.

Yet it is equally clear that however bizarrely her family behaves and however brutally she is mocked by smug Obama supporters, Palin remains an unsinkable star whom many Republicans are now gleefully comparing with Caroline Kennedy, who is bidding to take over Hillary Clinton’s New York Senate seat.

Kennedy, despite her political heritage, has turned out to be a stumbling performer with none of Palin’s charisma or charm. Not only has she failed to impress media interviewers, who have been reduced to counting her “um”s and “you know”s, but she has also fallen back on the same kind of barely coherent rambling for which Democrats pilloried Palin.

One Democratic congressman complained last week that Kennedy lacked the “guts and gumption” to succeed Clinton as senator. No one has ever said that Palin lacked guts or gumption. Perhaps they named the baby Tripp for the journey to Washington that the Alaska governor still seems determined to finish.

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