Sarah Palin is spending the week breaking the rules again. Everything about her “One Nation” bus trip, except the bus, is the antithesis of how most politicians would do what she’s doing. The question is whether she could ever run for president this way.

Palin is partway through her tour of symbolically important historical sites along the East Coast. After a weekend in and around the capital, she stopped at the Gettysburg battlefield and then saw Independence Hall and the Liberty Bell in Philadelphia on Tuesday.

She will get to New Hampshire, whose political significance is well-known, late in the week. But this is not, she has insisted, a political campaign. Still, the trip has renewed speculation that she could be heading in that direction, though no one but Palin and her husband, Todd, may know the real answer.

Those who have campaign experience say her un­or­tho­dox approach is a non-starter. Three senior Republican strategists dismissed the idea that the tour Palin and her family are on could be a prototype for a campaign. One called it “an ill-conceived” venture, and another said that although it gives Palin publicity without real scrutiny, it would not work for a candidate.

Palin wouldn’t have it any other way. No one enjoys tweaking the politico-media establishment more than the former Alaska governor, who believes she has been scorned and ridiculed by that establishment throughout her political career. In that context, running for president would be the ultimate antiestablishment act by the nation’s most unpredictable politician.

Of course, no one knows whether the bus tour is designed to lead to a candidacy or is just another way for Palin to capitalize on her celebrity. She has played that card repeatedly, and with considerable success, to enhance her personal brand, if not her political standing.

She manages to keep speculation about a 2012 presidential run alive through the most slender of hints. She has indicated that a future tour may take her to Iowa. Don’t be surprised if South Carolina pops up on her map at some point in coming weeks. Those stops alone would feed the story line that she might just possibly be thinking about considering whether to get serious about exploring a candidacy.

If nothing else, she has mastered the art of playing the media. She spent the holiday weekend in a game of cat-and-mouse with reporters, refusing to issue a schedule of her stops at historic sights. She spoke to reporters in Gettysburg on Monday night. She then ducked the media there Tuesday morning. She says she wants reporters to have to work a little to figure things out.

“I don’t think I owe anything to the mainstream media,” she told Greta Van Susteren of Fox News. “I think it would be a mistake for me to become some kind of conventional politician.”

The next stops on Palin’s tour include the Statue of Liberty, any number of places in Boston and then New Hampshire — but just when and where and where else is anybody’s guess.

But on a weekend when other real or likely Republican candidates were campaigning, she still drew the most attention. Former Minnesota governor Tim Pawlenty was in Iowa on Monday and Rep. Michele Bachmann (Minn.) was in New Hampshire. Palin overshadowed both, at least in media coverage. On Thursday, former Massachusetts governor Mitt Romney will formally announce his campaign. That will draw a crowd. Until then, Palin is taking up everyone’s space.

The tour looks as much like a summer vacation for the Palin family as a political event. “I’ve said from the beginning, this isn’t a campaign tour, except to campaign on our Constitution, our charters of liberty,” she said in her Fox News interview.

But it is not a journey that an ordinary family might take. Palin’s trip includes private tours of historic sites. The photo of her at the National Archives, posted Monday on, should be the envy of every tourist who ever tried to cram into that grand room with its vaults holding historic documents. Most visitors have to strain to get a look at the words. Palin had the room to herself to read and contemplate. That is just one more piece of evidence that she is different.

Think about what Palin is trying to perfect as the most unconventional of politicians. She has the ability to connect with people personally. She has, as one Republican said long ago, the ability to be interesting. Not everyone in the GOP field can make that claim. Although she has done little to convince her many doubters that she could or should be president, she retains a loyal and passionate following.

Beyond that, she has shown everyone else in politics the power of social networking and how it can be used to nurture a political base or shake up the debates on issues of the moment. She also can amplify her views with interviews on Fox News, where she remains a paid contributor. If not a seamless operation — or a foolproof way to run a campaign — it suggests that the old ways of doing business politically are not necessarily the only ways.

Palin knows that if she were to run for president, she would be surrounded at every turn by the media — a pack that she would think was out to stop her. She doubts that would help her get her message out. What she may be trying to determine on this bus tour is whether she can keep reporters at bay enough to interact with people and perhaps project a message. So far, the jury is out.

Alex Castellanos, a GOP strategist, said Palin may have already decided that, although her goal is to defeat President Obama, she is not the candidate to do so. Instead, she is choosing a role between “everything and nothing,” a position as an energizer. Her challenge, he said, is not whether to run but whether to lead. She is now the embodiment of Republican grievances, but that goes only so far.

“She just repeats what Republicans already believe, in an emotional and energetic way, true,” Castellanos said in an e-mail message. “But when she leaves, republican voters are left right where they were standing when she entered the room. She doesn’t take us anywhere. Until she does, her stature will continue to diminish, not because she is not running, but because she is not leading.”

In New Hampshire, Republican activists are divided about a possible candidacy. They wonder whether the role she is playing is the one best suited to her talents. Walt Shakford, a retiree who turned out to see Bachmann on Monday, said, “I would rather see her as a spokesperson for our politicians than a leader of our party.”

Palin may continue to play out this string, knowing she commands an audience. She has said this week that she does not think the Republican field is set. She hints that there is still plenty of time for her to get in, should she choose to do so. She may never say she is not running for president, assuming that at some point everyone will know it is too late. At that point, the story will become: Will she endorse? Palin as kingmaker — that, too, could go on for months.

Palin is not a political strategist, according to those who know her. She is a visceral politician who operates on instinct. The question is whether she really wants to play a role as a leader and a politician. That is the hard decision she faces.

Staff writers Rachel Weiner in Philadelphia and Sandhya Somashekhar in New Hampshire contributed to this report.