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WINDHAM, N.H. — Senator Ted Cruz spoke of New England common sense. He reminded the “Live Free or Die” state that it had “shocked this country” by supporting Ronald Reagan. He invoked the local environs while discussing Russian energy resources.

“Y’all understand a New Hampshire winter,” he said, though the temperatures on Tuesday were kind.

Catapulting into the first primary state after his victory in the Iowa caucuses, Mr. Cruz arrived at his first event on Tuesday with a message tailored to the setting and unmistakably familiar.

“God bless the great state of New Hampshire!” he said, in an echo of each of his Iowa event-openers, save for the state.

He ticked off the main planks of his platform — overhauling the tax code, repealing the Affordable Care Act — and disparaged the “Washington cartel.”

He grinned while recalling pundits’ predictions that he had “no chance” of prevailing in Iowa just before the vote, when polls showed him trailing Donald J. Trump.

And most pointedly, he took direct aim at his chief rivals, Mr. Trump and Senator Marco Rubio of Florida, denouncing each for shifting stances on immigration.

“We said virtually the identical things to the voters who elected us. But when we got to Washington, Marco and I took very, very different paths,” Mr. Cruz said in response to a question, noting Mr. Rubio’s work on a bipartisan effort that included a pathway to legal status for unauthorized immigrants.

He also wondered why no one had heard a word of concern from Mr. Trump, whose focus on immigration has helped frame the race, during the 2013 fight over the bill. “He could have sauntered over to the ‘Today’ show,” Mr. Cruz said.

For now, Mr. Cruz finds himself fighting for votes in a state where headwinds and tailwinds will whip at his candidacy in succession.

His success in Iowa seems likely to fuel Mr. Cruz’s central argument that conservatives should coalesce around his presidential bid. But the electoral terrain, in a state with more moderate leanings and fewer evangelicals, is less of a natural fit.

And after weeks spent insisting that the primary had become a “two-man race” with Mr. Trump, Mr. Cruz must grapple with Mr. Rubio’s stronger-than-expected finish in Iowa.

Speaking to reporters aboard his plane late Tuesday en route to Greenville, S.C., Mr. Cruz declined an opportunity to repeat his “two-man race” assessment.

“That’s going to be a question for the voters to decide,” he said, standing beside his wife, Heidi, on the charter he has nicknamed “Constitution One.”

Mr. Cruz has set his sights well beyond New Hampshire. His team speaks daily of its expansive footprint in the Super Tuesday states that vote on March 1.

Mr. Cruz boasted of his campaign’s impressive war chest; he said he ended last year with nearly as much cash on hand as Mr. Rubio, Jeb Bush, Chris Christie and John Kasich combined.

“The conservative is supposed to be broke,” he said, alluding to Rick Santorum and Mike Huckabee, who left Iowa with little money despite winning the previous two caucuses.

Before Mr. Cruz’s town-hall-style event in Windham, his spokesman, Rick Tyler, demurred when asked if the campaign expected to win in New Hampshire.

“We’re running here to exceed expectations,” he said. “I don’t expect to win.”

His stated prediction: Mr. Trump. (Of course, the Cruz campaign probably hopes to place the burden of high expectations on its rival.)

Other allies were less restrained. “It’s time we win,” said Robert C. Smith, a former New Hampshire senator who supports Mr. Cruz, repeating himself for emphasis.

Mr. Smith reminded the crowd that Pat Buchanan carried the state in 1996 and that Mr. Smith had won six congressional primaries in the state himself.

Mr. Tyler noted that “there are still evangelical votes” in New Hampshire. (The candidate’s stump speech on Tuesday included a familiar closing: asking voters to pray.)

Mr. Tyler also argued that several more moderate candidates were likely to splinter the vote among Mr. Cruz’s competitors. But he added that several other constituencies, from gun rights advocates to opponents of abortion, were likely to be attracted to Mr. Cruz.

Mr. Cruz has taken pains to honor local custom. On past visits, he has defended Tom Brady, the New England Patriots quarterback, amid a league inquiry. And since his Monday victory, he has name-dropped Dunkin’ Donuts, a New England-based fixture of local commerce, at least three times.

Among attendees, Mr. Cruz’s victory in Iowa — which has had little success in picking eventual nominees in recent cycles — seemed neither to galvanize nor to dissuade prospective Cruz supporters.

“I’m more pragmatic about it,” Chris Pessinis, 53, of Windham, said. He is still torn between Mr. Cruz and Mr. Rubio.

One albatross in Iowa, Mr. Cruz’s opposition to ethanol subsidies, seemed to have earned him admiration here.

That certainly would resonate with New Hampshire residents because of his trustworthiness, said Carl Johnson, 77, of Atkinson, N.H. “I like a lot of Trump’s ideas, but it is kind of pandering,” he said.

Near the end of his event in Windham, Mr. Cruz took stock of Mr. Trump’s escalation of hostilities in recent weeks, when he questioned Mr. Cruz’s eligibility for the presidency because of his Canadian birth and appraised him as a “nasty guy.”

“Six weeks ago, Donald Trump was saying every day that I was his friend, that he loved me, that I was terrific, that I was nice,” Mr. Cruz said. “And now I’m an anchor baby.”