There is a strange lack of activity inside Newt Gingrich's campaign headquarters in Iowa, the state which next month kicks off voting in the Republican party race to pick a candidate to face off against President Barack Obama.

Gingrich, an irascible former House Speaker with a notoriously high regard of himself, is the Republican frontrunner. He has suddenly jumped ahead in the Iowa polls, easily outpacing his more moderate rival, Mitt Romney. But inside his Urbanville headquarters – his only office in Iowa – there are rows of empty desks. It only opened a week or so ago and phone lines are also scarce. A handful of staffers are there, and one solitary volunteer, Judy Reynolds, a 64-year-old from Indiana, who gamely mans the front desk.

"It is a groundswell movement. It's moving up," said Gingrich's Iowa deputy director, Katie Koberg, sitting in the almost empty office. Reynolds also displays enthusiasm that belies the campaign's current lack of physical organisation. "Newt is going to pull all quadrants of the party together," she enthused, though she admitted Gingrich's rise surprised her. "It's where I prayed it would be, but I did not see it happening so fast," she said, admitting that a few days ago more volunteers had shown up to make calls but there were no phones for them to use.

The fact that the present Republican frontrunner, a man who could be next president of the United States, has such a shoestring operation in the vital first state to vote should not be a surprise. It should almost be expected in a Republican race that has been one of the strangest in modern US political history.

As the party lurched right under the impact of the anti-government Tea Party, it has desperately tried to ignore the charms of the centrist Romney. Instead a parade of extreme conservatives, from mogul Donald Trump, Minnesota congresswoman Michele Bachmann and Texas governor Rick Perry to pizza magnate Herman Cain, have swapped the anti-Romney torch. And, one by one, they flamed out in bizarre scandals and mis-steps. Cain's sexual escapades forced him out of the race. Perry's notorious "Oops" moment in a debate dented his chances.

Other debates were marked by Republican crowds booing a gay soldier in Iraq and cheering the idea of a sick man dying because he had not bought health insurance. "This is a circus that has come to town," said Professor Bruce Gronbeck, a political scientist at the University of Iowa.

Now it is Gingrich's turn at the top. He has already started to wobble, after having referred to himself as a "celebrity" and proposed to ease child labour laws to allow pupils in poor neighbourhoods to be janitors at their schools. They could learn the "work habit" by cleaning toilets, he suggested. Such comments are a sure sign the Republican race has plenty more shocking moments to come.

Newt Gingrich: the Republican frontrunner with a shoestring staff. Photograph: Brendan Hoffman/Corbis

The air of strangeness does not go away in the Romney campaign. In some ways it is the campaign that dare not speak its name – certainly not in Iowa, where Romney's well-funded, slick, highly organised effort has run up against a solid wall of conservative antipathy.

Last week Romney deployed one of his many powerful surrogates to hit the stump in West Des Moines on his behalf in the form of Chris Christie, the New Jersey governor, who is popular with conservatives but has ignored entreaties to enter the race himself. Instead Christie tried to persuade his Iowan audience of Romney's merits. "He is the only person who can legitimately take this fight to Barack Obama," he said.

That is a point echoed by polls that show Romney beating Republican rivals in match-ups with Obama. It certainly appeals to John Strong, a veteran who is backing Romney and came to see Christie to show his support. "He can win against Obama. He is not so far right and some Democrats would vote for him," he said. But that argument is having difficulty taking hold on Iowa Republicans and the party nationwide.

So Romney has gone on the offensive against Gingrich, making a TV ad that highlights Romney's solid marriage and family life. It seems sugar sweet, but is designed to prompt a debate on Gingrich's three marriages. Christie continued that fight, telling a long story of how much Romney's family and marriage meant to him.

But the rally was far from gaffe-free. First, was the unusual choice of location: a local firm called Kum & Go, whose name is ripe for mocking by late-night comedians. Then it was hit by protesters from the Occupy movement who started chanting that Romney was a tool of the top 1% of rich Americans. Christie ended up bellowing through his microphone at them, until security roughly hauled them out. Most worryingly for Romney campaign staffers was the Q&A session after Christie's pitch. Instead of asking about Romney, many voters asked Christie when he himself might run or praised his record in New Jersey. Christie gamely tried to keep things centred on Romney, but eventually gave up and discussed his own ambitions, conceding that he might run in 2020 (after Romney's two terms, of course). He got a huge cheer.

Nor do Romney's woes – and conservative Republicans' dreams – end with Gingrich's rise. One recent poll showed Romney had finally moved out of second place in Iowa – but to third, behind the insurgent grassroots effort of libertarian-leaning Texan congressman Ron Paul. Paul is vilified by both his own party and the Democrats for his blend of social liberalism, stern critique of US foreign policy and extreme fiscal conservatism. But there is an undeniable wind in his campaign at the moment, as his Iowa poll numbers hit 18%. Paul has made a virtue of treks through Iowa's small towns, drawing strong support among college students.

It was no different last week in Boone, a typical slice of Americana deep in the heart of Iowa's frozen rural heartland. Paul had packed out a room at Boone's public library. His speech blended right and left. "The first year I will cut a trillion dollars out of the budget," he said, outlining plans to axe five federal departments. That is red meat to conservatives. But five minutes later he called for the return of all US troops abroad, from Germany to Afghanistan: a policy that even the most leftwing Democrat would not dare utter.

No one should write Paul off in Iowa. In the topsy-turvy race of 2011 he could easily provide a final upset. "He's doing great," said local Boone internet developer Ryan Twedt, 27.

"The Republican party is in a pickle," said Gronbeck. "They rush around from one candidate to another, discarding one this week and then another next week." But to many Iowans – and Americans at large – the ups and downs of the Republican race have been bewildering. The US has deep problems. Obama is far from popular, as the headline jobless rate stays near 9%; the real rate is far higher. Growth is anaemic. Consumer confidence is low. Poverty is spiralling upwards.

One Iowa town has come to symbolise the problems. Newton, about 20 miles from the state capital of Des Moines, was a "factory town" centred on Maytag, a washing-machine firm. But the firm moved manufacturing to Mexico. Then sold its plant. Then, in 2007, it closed. That cost 1,800 jobs in a town of just 15,000 people.

Paul Mattingly, who owns a music store on Newton's pretty town square, has little time for the Republican candidates. He believes the wacky, wild, weird race has failed to tackle Newton's problems or those of the US. "There is no one in the GOP field who makes any sense to me," he said. But he acknowledged the seriousness of what was happening. Whoever the Republicans settle on – whether Romney or a conservative alternative – will battle for the White House against an incumbent hamstrung by economic malaise.

"It's been a spectacle. But I am scared one of them will actually win," Mattingly said.

• This correction was published on 18 December 2011:

Republican presidential candidate Newt Gingrich has his headquarters in Urbandale, Iowa, not Urbanville ("From Mitt to Newt: Iowa left bewildered", News).