WINDHAM, N.H. — With his wife introducing him as a man raised equally on the Bible and the Constitution, Iowa caucus winner Ted Cruz began his final New Hampshire push by positioning himself as the presidential candidate for true conservatives as well as the religious right.

At a packed rally in an evangelical church Tuesday, Cruz began with “God bless the great state of New Hampshire’’ and ended by quoting Scripture. In between, though, he draped himself in the conservative mantle of Ronald Reagan and even quoted a more secular Granite State hero, two-time Republican primary winner John McCain.

Until now, Cruz, the Republican US senator from Texas, has spent less time and money in New Hampshire than some rivals, focusing on states more heavily populated with evangelicals. But he is determined not to stumble here like the last two Iowa winners did — Mike Huckabee (2008) and Rick Santorum (2012) drew significant Christian support while winning Iowa before finishing third and tied for fourth, respectively, in the Granite State. Cruz has 16 New Hampshire stops planned during the final week.

Clad in a flannel work shirt and jeans, Cruz took the stage Tuesday afternoon to cheers from the elbow-to-elbow crowd at Crossing Life Church and immediately invoked Iowa.

“So, what a victory last night!’’ he said, while taking a jab at pundits. “The men and women of Iowa sent notice that this election is not going to be decided by the media.’’

It was hardly lost on Cruz that no nonincumbent Republican has ever won both New Hampshire and Iowa in the same year. He quickly referenced 1980, when Ronald Reagan lost Iowa to George H.W. Bush but rebounded to take New Hampshire. Though Cruz won Iowa, he cast himself here as the heir to Reagan in a crowded field.

“Back in 1980 all the media said, ‘This guy Reagan, he’s a crazy right-wing kook, he’s too extreme, and by the way, he’s really down in the polls,’ ’’ said Cruz, as the crowd picked up the inference to his own campaign. “But you know what, the Granite State took a look at Reagan and said, ‘That guy believes what he’s saying. . . . He tells the truth, and he’s going to do exactly what he says.’

“The Granite State shocked this country by giving Reagan the victory, and literally the men and women of New Hampshire changed the course of history,’’ Cruz said. “Your actions liberated billions from bondage, won the Cold War, tore the Berlin Wall to the ground — that’s what New Hampshire did. And Washington doesn’t like that.’’

Evangelical voters and hard-right conservatives combined make up one-fifth of the typical Republican primary electorate in New Hampshire, where voters are traditionally more moderate and secular than in Iowa, said Dante Scala, a University of New Hampshire political science professor and coauthor of a book on the different factions of the Republican Party.

“He’s definitely appealing to a niche audience here,’’ said Scala. While Cruz has a “definite ceiling’’ on his New Hampshire vote total, he could surpass Huckabee and Santorum. “They were appealing to social conservatives and religious conservatives, but Cruz can also make the case that he can appeal to those more secular conservatives, as a quasi-libertarian.’’

And amid a crowded field, even a 20-percent share could mean second place, Scala said.

“New Hampshire is the icing on the cake for Cruz, but clearly South Carolina is where his next big test is,’’ he said. “Even if he finished fourth it doesn’t mean that South Carolina is out of reach.’’

In the church Tuesday, amid a sea of Cruz stickers and “Don’t Trust the Liberal Media!’’ placards, Cruz’s supporters included self-described libertarians and 1980 Reaganites as well as evangelicals.

Leaving with an autographed poster, Don and Cecile Simard, both 80 and former Reagan supporters from Nashua, said they were leaning to Cruz — Cecile for his tough talk against ISIS, Don for his limited-government conservatism.

Ross Hogan, a 36-year-old who works in cybersecurity, said he considered Rand Paul for his libertarianism, flirted with Donald Trump this time for his emotional appeal, and mulled Marco Rubio for his potential electability — before picking Cruz a week ago.

“What really appealed to me is his vision of liberty, his vision to adhere to and uphold the Constitution, and the fact that I feel I can believe what he says,’’ said Hogan, who lives in Londonderry. “A lot of candidates talk a big game, but the proof is in the pudding, and Senator Cruz has lived up to what he says.’’

Eric Moskowitz can be reached at eric.moskowitz@globe.com. Follow him on Twitter @GlobeMoskowitz.