Former Florida governor Jeb Bush poses after speaking Friday at the Republican Leadership Summit, where nearly 20 potential GOP contenders made their case to party activists. (Darren McCollester/Getty Images)

Saint Anselm College has been a required stop on the pilgrimage for presidential aspirants, going at least as far back as John F. Kennedy and Richard M. Nixon more than a half-century ago.

When former Florida governor Jeb Bush (R) made his first speech here on Friday, he pointed to the historic photos on the wall.

“I’m looking out at this room, and I’m seeing these incredible pictures, some of which bring back really fond memories — guy over there, guy over there,” Bush said.

They were decades-old images of two former candidates who happened to be Bush’s father and brother.

The lessons that George H.W. Bush and George W. Bush had learned in New Hampshire were hard ones. Both stumbled the first time they ran here, in 1980 and 2000, respectively.

At a “Politics and Pies” event in Concord, N.H., former Florida governor Jeb Bush had a rare treat: blueberry pie. The presumed Republican presidential candidate generally sticks to snacks on a strict “paleo” diet. (Ed O'Keefe/The Washington Post)

For Jeb Bush, an even trickier set of challenges awaits in the Granite State in 2016. The first-in-the-nation primary may well be a do-or-die situation for the third Bush to run in it.

Not yet formally declared as a candidate, Bush already is being seen as the establishment front-runner. But that status means less than it used to, given that the GOP has moved further to the right than it was when the older Bushes ran. It also appears that Jeb Bush will be running in a far larger field of credible, well-financed contenders.

Even more significant, New Hampshire could be a crucial test of Bush’s core argument that he is the GOP candidate who stands the best chance of beating Democratic front-runner Hillary Rodham Clinton in the general election.

Unlike in the first contest in Iowa, which are caucuses likely to be dominated by social conservatives hostile to Bush, New Hampshire’s primary electorate will include independents. In fact, there will probably be more of them voting in the Republican primary than usual, if the Democratic race remains as uncompetitive, as it now appears.

For a candidate such as Bush, “this is where you’ve got to perform,” said Thomas D. Rath, a former Republican National Committee member from New Hampshire who has been a senior adviser to presidential campaigns since the 1980s.

“You walk a tough line if you’re Jeb,” added Rath, himself not yet committed to a candidate. “A lot of people who were involved with his father and brother are not visibly involved here.”

Even such Bush family stalwarts as former New Hampshire governor John H. Sununu are remaining on the sidelines for now.

“I’ve got five or six really good friends in this thing,” Sununu said in an interview. He is not sure whether he will go to work for any of them, although “I’ll know a lot better in June, July or August.”

Making a strong play for parts of Bush’s business-friendly coalition is Wisconsin Gov. Scott Walker, who leads the latest polls in New Hampshire. Sen. Rand Paul (Ky.) is another rising candidate with a viable path to victory — his father, Ron Paul, placed second in the 2012 New Hampshire primary, and the senator has inherited much of the elder Paul’s network.

Also competing vigorously with Bush is New Jersey Gov. Chris Christie, who held a series of town-hall meetings last week. Ohio Gov. John Kasich — whose pitch and profile have similarities to Bush — appeared in Nashua on Saturday.

Next year, while Iowa is likely to decide who emerges from the right, New Hampshire will be the state that winnows the choices for the GOP’s country club and chamber of commerce wings that usually embrace center-right candidates. Christie’s dogged approach, Kasich’s possible entry, Paul’s roots and Walker’s broad appeal complicate Bush’s chances of coming away with a convincing victory in the primary.

Republicans also are wary of any whiff of presumption on Bush’s part — as Lisa Mediano, a lawyer from Fitzwilliam, N.H., bluntly told him at a GOP gathering over the weekend in Nashua, where no fewer than 17 declared or potential presidential contenders spoke.

“I hope there is more of a fight,” Mediano said. “I don’t want a coronation on our side.”

Bush drew chuckles from the audience as he replied: “I don’t see any coronation coming my way, trust me. . . . I’m really intimidating a whole bunch of folks, aren’t I?”

Democrats will also be watching Bush’s New Hampshire effort closely, as a sign of how much of a free-for-all the GOP nominating process is likely to become.

“Jeb Bush has to win New Hampshire. It’s a must-win for him, because he will lose Iowa. You’ve got to win one of them, particularly if [you’re] considered to be something of a front-runner,” Democratic strategist James Carville said at a panel discussion in February celebrating the New Hampshire primary’s upcoming 100th anniversary.

“I will go further,” Carville said. “If Jeb Bush loses New Hampshire, they’ll get Mitt Romney back in the race” — a reference to the GOP’s 2012 nominee, who briefly flirted with the idea of making a third bid for the White House.

So far this election cycle, Bush has made only two swings through the state, compared with a half-dozen or more by such likely rivals as Christie, Texas Sen. Ted Cruz, former technology executive Carly Fiorina, Paul and former New York governor George Pataki.

“The first 50 [visits] is just the intro” in a state that expects to see presidential candidates early, often and everywhere, said Republican National Committee member Steve Duprey, a former state party chairman.

That Bush is lagging in that area is not a problem — at least not yet, political veterans say.

“Right now, he’s absolutely fine,” Rath said. “But at some point in time, it’s going to start to close, and people are going to start making choices. On Memorial Day, we’re going to be in a different place than we are now. And by July Fourth, we’re going to be in a very different place than we are now.”

Rep. Peter T. King (R-N.Y.), a Long Island moderate who has made nine New Hampshire visits as he considers his own 2016 bid, said Bush “realizes that he’s going to have to fight hard to get it.”

“He’s not like Hillary Clinton, thinking he’s entitled. Or, quite frankly, like George W. Bush in 2000, who never saw John McCain coming. Bush got caught off guard in New Hampshire, and you better believe Jeb remembers,” King said.

George W. Bush managed to recover his footing in later primaries after his 18-point loss to the Arizona senator. He even won New Hampshire in the 2000 general election — which was the last time a Republican carried the state.

His father, in 1980, was not so lucky. The brief burst of momentum that George H.W. Bush got from winning Iowa fizzled when he lost New Hampshire. Eight years later, he took a page from Ronald Reagan’s playbook, emphasized New Hampshire over Iowa, and scored a victory here that helped snuff out the campaign of Sen. Robert J. Dole (R-Kan.).

Clinton, in a nod to New Hampshire’s importance in the general election, will swing through on Monday and Tuesday. The visit will also be a reminder of her come-from-behind win here in 2008, which was the emotional high point of a nomination battle that she ultimately lost to Barack Obama.

Her arrival will also evoke what bothers many about Bush’s candidacy.

At a Republican “politics and pie” event in Concord on Thursday night, retiree Bill Doherty asked the former Florida governor: “With 300 million people in the country, why should only two families produce the leaders in our country? It’s a question I’m sure you’re going to face in other places. How do you answer that?”

Bush replied that he has “enough self-awareness” to recognize that is “a serious question” and joked that he is not trying to “break the tie between the Adams family and the Bush family,” each of which produced two presidents.

“Campaigns tend to be about the future,” Bush said. “I want to show my heart. I want to show I care about people. I have a proven record of doing that in my life, as well as in government.”

In that hour-long appearance, Bush ticked off his accomplishments as Florida governor. He held his ground against pointed questions about his support for sweeping immigration overhauls and Common Core educational curriculum standards, both of which are anathema to many conservatives.

By the end of it, Doherty went from being skeptical to sold on Bush.

“I see a guy who is articulate without being glib, who is willing to stand up for what he believes in and not back down,” Doherty said. “I absolutely would vote for him after I’ve heard him.”

And that is how Bush or anybody else has to win in New Hampshire — one Bill Doherty at a time.

Ed O’Keefe contributed to this report.