PARKERSBURG, Iowa — Running as an underdog presidential candidate isn’t always glamorous.

You speak to half-filled halls and small rooms, low-key rallies. There may not be a bus emblazoned with your smiling face. And then there are the rally-goers who blatantly say they aren’t quite convinced.

But for the longshots sprinting across Iowa and New Hampshire before the Feb. 1 caucuses, one thing keeps them fired up: the prospect of a political upset.

“Let’s prove the New York media totally wrong,” former Arkansas Gov. Mike Huckabee said to about 40 people gathered in a senior center dining room in Parkersburg, Iowa, last week. At least half were residents finishing dinner, a couple of whom left in the middle of the town hall-style meeting.

Among those hoping for an Iowa winter miracle are Huckabee, 2008 winner of the caucuses, and former Pennsylvania Sen. Rick Santorum, winner in 2012. Also looking for political salvation in either first-to-vote Iowa or in the New Hampshire primary are Kentucky Sen. Rand Paul and former technology executive Carly Fiorina.

Polls in both states show them all lagging in the low single digits. Texas Sen. Ted Cruz and businessman Donald Trump are leading the recent polls in Iowa, followed by Florida Sen. Marco Rubio and, retired neurosurgeon Ben Carson in third and fourth.  Former Florida Gov. Jeb Bush, New Jersey Gov. Chris Christie and Ohio Gov. John Kasich are behind in Iowa, but running stronger in New Hampshire.

Some other underdogs have left the race already. Remember former Louisiana Gov. Bobby Jindal, former Texas Gov. Rick Perry, South Carolina Sen. Lindsey Graham and former New York Gov. George Pataki?

The tricky thing for many of these candidates is that having fans in the early states doesn’t necessarily translate into votes.

John Stewart, a 64-year-old attorney who lives on Lake Panorama in Iowa, said he liked Huckabee and Santorum, but he didn’t believe they had a chance at winning.

“Their day has come and gone,” he said at the Prime Time restaurant in Guthrie Center, Iowa before a Cruz event last week. “People still like and appreciate them. But Cruz and Rubio have some momentum. Cruz has more. It’s Cruz’s time.”

Huckabee, whose slipping poll numbers bumped him off the main stage event during the last Republican debate, noted that many people don’t make up their minds until the final days. But he also called Iowa a “critical ground zero.”

“I don’t want to say we have to be one, two, three, four. A lot of it depends on where the grouping is,” Huckabee said.

Upsets are a grand tradition of the Iowa caucuses. Huckabee and Santorum both came from behind to win. But this year, Trump and Cruz seem to have captured many of the conservative and evangelical voters that supported them previously. Of course, there are lots of reasons a candidate may stick around. Some want to advance their political philosophy or promote their brand for future book deals and TV appearances. And there’s always the prospect of a cabinet role or the vice presidency.

Still, second-time candidate Santorum, who wooed over 45 people gathered at a house party in suburban Des Moines Thursday, said he believes in the voters of Iowa.

“Three and half weeks is a long time,” Santorum said, as a group of friends and neighbors mingled and munched on Chex mix and cookies. “Four years ago, fifty percent of the people who voted didn’t decide until the last week.”

Despite narrowly beating eventual nominee Mitt Romney in Iowa in 2012, Santorum has spent this entire race at the back of the pack. He’s never polled well enough to make it on to the main debate stage and has focused largely on Iowa, spending so much time here that he had visited all 99 counties by September.

The Republican debates have proven particularly frustrating for the lower-polling candidates. This week, Fiorina and Paul were cut from the main stage at the Republican debate in South Carolina Thursday. Debate host Fox Business Network announced the debate lineup Monday evening.

Paul said last week before a birthday celebration in a Des Moines bar the race was still “wide open.” He stressed his organization on college campuses and noted that he has volunteer captains in over 1,000 of Iowa’s 1,681 precincts.