Sen. Ted Cruz addresses the crowd at a town hall event at Crossing Life Church in Windham, N.H. (John Tully/For The Washington Post)

Sen. Ted Cruz, energized by his evangelical-fueled victory in Iowa, set out Tuesday to defy recent history and finish well enough in next week’s New Hampshire primary to carry him to the Republican nomination.

Cruz’s challenge is to prove that, unlike the past two GOP winners of the Iowa caucuses, he can expand his base here and nationally. While the campaign said it has more than 1,000 volunteers in New Hampshire, that is far fewer than the 12,000 who helped Cruz triumph Monday in Iowa, and the evangelical base here is much smaller.

“We’re running here to exceed expectations,” campaign spokesman Rick Tyler told reporters before the senator from Texas took the stage here. “No, I don’t expect to win. No.”

But Cruz does hope to damage his opponents, particularly Donald Trump and Marco Rubio, who finished behind him in Iowa. He told a packed town hall meeting here that Trump was absent in the fight against “amnesty” for immigrants who are in the country illegally until he discovered that it was “a good issue,” and he said Rubio had broken his promises on the same topic.

After weeks of saying the race was a two-man contest between himself and Trump, Cruz backed off the assertion Tuesday when asked if it is now a three-man race, including Rubio.

How rural voters controlled the Iowa caucuses

“That’s going to be a question for the voters to decide,” he told reporters aboard his plane headed to a rally in Greenville, S.C. “That’s going to be a question for the voters in New Hampshire to decide, for the voters in South Carolina to decide.”

At the New Hampshire event, Cruz repeatedly compared himself to former president Ronald Reagan, reminding his audience that the state backed Reagan in 1980 (but not mentioning that he lost the Iowa caucuses that year).

“The Granite State shocked the country,” he said, telling the crowd that voters here helped Reagan change the course of the United States and the world by toppling communism and liberating millions.

Cruz also demonstrated in his first post-Iowa speech that he will stick with the strategy that has brought him this far, putting faith at the center of his message. After warning several times that America is at cliff’s edge, he asked the audience to pray to “awaken the body of Christ to pull us back from the abyss.”

After investing so much effort in Iowa — a bet that paid off better than many pollsters had predicted — Cruz’s campaign is trying to transition to the landscape of New Hampshire. Its headquarters in Manchester is a modest affair, tucked at the back of a building that also houses a business selling fireplaces. A half-dozen workers manned computers and phones when a reporter stopped by Tuesday morning; a staffer said many volunteers were out knocking on doors.

The campaign wants to avoid the fate of Mike Huckabee and Rick Santorum, who won the Iowa caucuses in 2008 and 2012, respectively, but lost New Hampshire and their bids to become the GOP nominee.

Speaking in Windham, N.H., the day after the Iowa caucuses, Republican presidential candidate Ted Cruz slammed rival Donald Trump, saying that three years ago he supported amnesty for people who came to the United States illegally. (Reuters)

The Cruz campaign hopes that the Iowa win will help goose fundraising, and Tyler emphasized that Cruz can repeatedly go back to his small-donor base and ask for new contributions. On the big-money side, a network of super PACs could raise millions more.

The Iowa results energized Cruz and the town hall crowd of more than 200 people, who gave him a standing ovation as he entered the room. “What a victory last night!” the senator said. “Two nights ago I was watching TV . . . every pundit said there’s no way Cruz can win. It can’t happen, it’s impossible, the race is done. But last night the men and women of Iowa sent notice across this country that this election is not going to be decided by the media. . . . It’s going to be decided by the grass roots.”

Cruz aimed much of his criticism at Trump, who is leading in the polls here and has questioned whether Cruz, who was born in Canada to U.S. citizens, meets the constitutional requirements to be president. Cruz has said there is no question he is qualified.

“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, and now I’m an ‘anchor baby,’ ” Cruz said, using a term for a child born in a country for the purpose of gaining residency or citizenship for his family. “What did change was his numbers started going down, and my numbers started surging.”

As for Rubio, who finished in a strong third place in Iowa, just behind Trump, Cruz slammed him for working with Sen. Charles E. Schumer (N.Y.) and other Democrats on a comprehensive immigration bill that would have provided a path to citizenship for up to 11 million people. Rubio has since disavowed the legislation.

Cruz said that the bill “was directly contrary to what Marco promised the men and women who elected him.”

Robert Boots, a retiree from Windham who attended the rally sporting a Cruz sticker, said in an interview that he was attracted to the Texan because of his Christian faith and his views on national security and the economy. Boots said he believes that Cruz will do better than expected in the Feb. 9 primary here — perhaps a strong second — but agreed with the conventional wisdom that Trump will win.

“It’s all over the map,” Boots said of New Hampshire’s Republican electorate.

The Cruz campaign says it plans to rapidly expand its volunteer base here, opening a dorm for out-of-staters as it did in Iowa and South Carolina. The volunteers are attempting to rustle up support using the campaign’s analytics system, which sifts data to try to find people who are likely to vote for Cruz.

Tyler said the campaign plans to base its strategy on what worked in Iowa, matching a volunteer army with a disciplined turnout machine.

“So we’ve proven that we can turn out evangelicals in Iowa, and we’re going to take that model, with that organization, and replicate that through the states,” Tyler said. “But in the meantime we’re going to compete here, and we’re going to compete here hard.”

Juliet Eilperin in Washington contributed to this report.