Campaigning in Waukee, Iowa, Republican presidential candidate Chris Christie told two personal stories about addiction and said he wants the GOP to be “pro-life for the whole life.” (Chris Christie)

Chris Christie is the consummate New Hampshire candidate, all the way down to his silver lapel pin in the outline of the Granite State.

Yet this week the New Jersey governor was in a relative wilderness, caravaning along the slushy roads of eastern Iowa and sporting a different pin on his suit jacket: the Iowa state flag.

“I want your vote,” Christie told a hundred Iowans bundled up inside a coffee shop here Tuesday morning. “I’m not here just to get a Fox News show or a book deal or something else. I want to be president.”

While New Hampshire remains the hub of activity for Christie and other establishment-favored Republican candidates, including former Florida governor Jeb Bush and Sen. Marco Rubio (Fla.), Iowa has suddenly emerged as a playground of opportunity, where an intense and stealthier battle among them is getting underway.

None of the establishment candidates expects to win Iowa, but associates of Christie, Bush and Rubio see an opportunity for a victory of momentum — and positive media coverage — for whomever can capture the most mainstream Republican support. That faction, which the campaigns see as up for grabs, is estimated at anywhere from 20 to 35 percent of the electorate.

Sen. Marco Rubio (R-Fla.), left, accompanied by his wife Jeanette, right, and their children, Anthony, 10, bottom center, and Dominic, 8, second from right, campaigns Tuesday in Clinton, Iowa. (Andrew Harnik/AP)

“There’s a lot to be won out here,” said David Kochel, Bush’s chief strategist and a veteran Iowa operative. “It’s probably the most undecided bloc of voters that you could find. It shows up in every poll, and I think they’re coming largely out of this lane. People wait, they kick the tires, they see who comes, they go to town halls, and they make up their minds late.”

The moderates have another motivation: to somehow slow Sen. Ted Cruz of Texas and Donald Trump, who have dominated the polls here for weeks. Many Republican leaders worry that if the two win big on caucus night, they could be hard to stop elsewhere.

A wild card could be Rubio, who has crossover appeal and is trying to position himself to take a run at Trump and Cruz. The Florida senator has four offices in the state and traversed it this week with his wife, his four kids and his latest high-profile backer, Rep. Trey Gowdy (R-S.C.).

“I hope to earn your support in the caucuses,” Rubio said Tuesday at a town hall meeting in Waterloo. But, he added, “I know you have a lot of choices.”

The voters the establishment candidates are going after in Iowa, including business people and farmers, are described by the campaigns as motivated more by economic interests and perceived electability against Democratic front-runner Hillary Clinton than by conservative ideology. They also make up the political base of Terry Branstad, the state’s even-tempered and long-serving Republican governor.

The Branstad coalition has forcefully reasserted itself in local politics the past few years but is splintered in the presidential race. The governor has stayed firmly on the sidelines. Many figures in his orbit, such as his 2014 reelection campaign senior staff, some top fundraisers and daughter-in-law Adrianne, are working for Christie, while some others, including Kochel, are helping Bush.

Douglas E. Gross, an unaffiliated Iowa Republican leader, said that unlike in 2012, when mainstream Republicans united behind Mitt Romney and nearly helped him win, this cycle they “have been sitting there forever without a candidate of their own.”

Iowa voters listen to New Jersey Gov. Chris Christie campaign at Elly’s Tea and Coffee House Tuesday in Muscatine, Iowa. (Andrew Harnik/AP)

David Axelrod, a Democratic strategist who helped run President Obama’s 2008 and 2012 campaigns, has been closely watching the GOP scene in Iowa. He said the establishment free-for-all here, as well as in New Hampshire, is particularly threatening to Rubio.

“If he gets dumped into fourth or fifth place in both of these states, maybe he lives to fight another day, but I can’t think that’s helpful,” Axelrod said. “He’s right now the flavor of choice among the conventional thinkers, but he’s got to do reasonably well.”

Stuart Stevens, who served as Romney’s chief strategist in 2012, cautioned that the jockeying to finish in the top tier in Iowa might not matter as much as some of the campaigns may think.

“My theory is that unless you actually win a state, it doesn’t really help you much. I don’t buy that second or third helps you. I don’t think anyone cares,” Stevens said.

Of the establishment contenders, Rubio has been performing the strongest, running third behind Cruz and Trump with 12 percent in the Real Clear Politics average of recent state polls. Bush is at 4.8 percent, and Christie is at 2.3 percent. Ohio Gov. John Kasich, another establishment candidate, is at 1.5 percent, though he has had a more limited presence in Iowa.

Craig Robinson, the founder and editor of IowaRepublican.­com and a former state GOP operative, said of the establishment dynamic: “It’s the most interesting race in Iowa, to be quite honest. I don’t think Rubio has put enough distance between himself and the Christies and Jebs of the world. That leaves the door cracked open.”

This explains why Christie spent two full days campaigning in Iowa this week. (He planned a third but scratched his Monday events after a snowstorm caused his flight to be canceled; he instead drove four hours from Chicago O’Hare International Airport.)

In January, Christie said, he intends to “evenly split” his time here and in New Hampshire. That would represent a change from what has been a New ­Hampshire-heavy schedule.

As in New Hampshire, Christie’s favorability ratings here have improved in recent months, while his Iowa campaign has quietly built an organization on the ground.

Christie sees an opportunity to spring a surprise on the pundit class by gobbling up mainstream caucus votes. He is eyeing places such as Cedar Rapids, Davenport, Dubuque and Des Moines: eastern and central Iowa cities where Republicans are more business-minded and less hard-line conservative than in the evangelical strongholds further west or in rural areas.

“We’re under no illusions about how difficult Iowa is, but we certainly feel like we can compete and improve,” said Mike DuHaime, Christie’s strategist.

Bush is perceived to have the most seasoned organization. Many GOP figures here are loyal to his family, having worked on the campaigns of his father and brother, both former presidents, going back to 1980. Bush’s super PAC, Right to Rise, has invested substantially here, blanketing the state with television advertisements for several months.

So far, these efforts have not paid dividends. His campaign announced Wednesday it had canceled its advertising plans in Iowa, a sign of its difficulty raising money, but is expanding its staff in the state to 20. Bush’s allied super PAC will continue airing ads. Although Bush increasingly has focused his campaign time in New Hampshire, he plans to make a three-day swing across Iowa beginning Jan. 11.

Bush is chasing voters such as Steve Schwemm, 66, a retired teacher who is a Republican but resists the hard-line conservatism of candidates such as Cruz. Schwemm said he is open to supporting Bush but doubts he has a chance at winning the nomination, so at the moment Schwemm is more intrigued by Rubio and Christie.

Taking his seat at the Waterloo Center for the Arts to watch Rubio campaign, Schwemm said: “I think he’s very electable. He’s a great debater, and in this day and age, that’s a skill you have to have. I think he’s young, dynamic and energetic.”

Then again, he said, “I like the straightforwardness of Chris Christie. I really do.”

Schwemm was undecided, with the caucuses 34 days away.

Costa reported from New York.