Sen. Ted Cruz defeated Donald Trump in Iowa on Monday night, but he faces a strikingly different set of challenges in trying to replicate that victory in New Hampshire’s primary next week. He has a lesser organization here, has spent less time here, and can’t count on such a large evangelical electorate.

History provides a clear warning. In 2008 and 2012, Mike Huckabee and Rick Santorum won the Iowa Republican caucuses with heavy support from evangelicals. Both then arrived here lacking a strong organization, lost this state and failed to become the GOP nominees.

With the Republican Party’s focus on Iowa now complete, the spotlight on ethanol and evangelicals is out. Now begins an eight-day sprint that in many ways will be entirely different because New Hampshire’s voters reflect a very different side of the GOP. They’re socially moderate and fiscally frugal, and use a primary voting system that allows greater participation by independent-minded voters who revel in upsetting the conventional wisdom.

It’s why a handful of GOP “establishment” candidates who did poorly in Iowa think they’ll perform better here.

“New Hampshire voters reset elections. That’s what you all do. . . . The reset starts here tonight,” former Florida governor Jeb Bush defiantly told about 300 supporters at Manchester’s Alpine Club on Monday night.

New Jersey Gov. Chris Christie told a crowd in Hopkinton Monday night that Iowa “has passed the ball to you.” The field would soon be thinned. “You all,” he said, “are going to decide it.”

Ohio Gov. John Kasich told an audience of about 200 at Bow Elementary School on Sunday that “you come here, and you look and you poke, once in a while you smell and you try to decide, is this our leader? Whether I win or not, I believe in this process. I believe that folks in New Hampshire are the best screeners that America can have to recommend to the country.”

Wayne Lesperance, a professor of political science at New England College in Henniker, N.H., said that “New Hampshire has gone differently than Iowa in six of the last nine elections on the Republican side, so the idea that one follows the other’s lead just doesn’t bear out.”

And yet, Iowa and New Hampshire share more in common this cycle, thanks to Donald Trump. He has held a double-digit lead over his GOP opponents here for more than 30 weeks and dominates the headlines — just as he did in Iowa before losing to Cruz there on Monday.

Cruz’s first place finish in Iowa and a stronger-than-expected showing for Sen. Marco Rubio of Florida, just behind Trump, could immediately scramble the top tier of the race.

Here are reactions from seven presidential candidates on the evening of the 2016 Iowa caucuses. (Sarah Parnass/The Washington Post)

For now, Trump is favored by 38 percent of GOP primary voters in New Hampshire, according to a Boston Herald-Franklin Pierce University poll released Sunday. Cruz is a distant second at 13 percent, followed by Rubio and Bush, 10 percent; Kasich, 8 percent; and Christie, 5 percent.

A CNN-WMUR-TV poll released Sunday showed similar results: Trump with 30 percent, followed by Cruz, 12 percent; Rubio, 11 percent; Kasich, 9 percent; Christie, 8 percent; and Bush with 6 percent.

New Hampshire Republican polling “has been stable for months now,” Dante Scala, an associate professor of political science at the University of New Hampshire, said by email. Surveys have shown “only minor shifts” among the “establishment” candidates — Rubio, Bush, Kasich and Christie — making it difficult to track any widespread switch in support from one to the other, he said.

Neil Levesque, executive director of the New Hampshire Institute of Politics at Saint Anselm College, agreed, saying that if any of the four establishment candidates can find a way to jump ahead in New Hampshire, this will shake up the entire race.

That’s why Bush, Christie, Kasich and Rubio see New Hampshire as their last opportunity to emerge as the anti-Trump.

While Rubio placed a strong third in Iowa, the other establishment candidates trailed far behind. Bush earned 3 percent support, topping Christie and Kasich, who each earned 2 percent.

In New Hampshire, Kasich held his 89th town hall meeting on Monday night. Christie has held 114 public events in the state since launching his campaign in June. Bush, who has most relentlessly attacked Trump as unqualified to be president, hosted his 80th public event in the state on Monday night. Rubio has been in New Hampshire less frequently, but is certain to earn renewed interest starting Tuesday.

Supporters of the New Hampshire primary process like to remind skeptics that they have more often picked the Republican nominee in recent years than Iowa. In 2008, Sen. John McCain of Arizona won here, and in 2012, former Massachusetts governor Mitt Romney won the New Hampshire primary. Both won the nomination.

Aside from social issues and state-specific interests, one of the biggest differences is that it is far easier to vote in New Hampshire. Iowa’s caucus system requires hours of time at local meetings and commitments to a political party. The caucuses don’t directly determine which candidates gets delegates. It is an expression of preference that must be ratified months later at state party meetings.

That has led many New Hampshirites to look down on the Iowa caucuses, a view most famously summed by Republican former governor John H. Sununu, who once said that Iowa picks corn and New Hampshire picks presidents. Many people here in both parties agree.

“I’ve yet to ever run into a New Hampshire voter who says, ‘Nah, I was going to vote for you, but your guy finished fourth instead of third in Iowa.’ They don’t exist up here,” said John Weaver, a top consultant to Kasich’s presidential campaign who advised McCain during previous primaries. “If you work hard, as the governor has done, and you put deep roots in the state, as we have done, you have to feel pretty good about withstanding whatever happens.”

David Price of Weare, N.H., attended Kasich’s event Sunday at the school and said he would take note of how Iowa voted. “But as a true New Hampshirite, I look at it independently,” he said.

Price called Kasich “a very personable individual” but added that right now “I’m leaning to . . . Jeb Bush.”

Arthur Moore, a retired physician from Bow, said he planned to learn more about Kasich but is also considering Bush and Rubio. Whomever Moore chooses, he said that “they’ve got to get rid of Trump — he’s a loose cannon, he’s a narcissist.”