CONCORD, N.H. — Ann Kuster, the daughter of two New Hampshire politicians, has been involved in the state’s presidential campaigns since 1972 and has played key roles in the campaigns of John Kerry and Barack Obama.

Democratic presidential candidate Sen. Cory Booker, D-N.J., addresses supporters outside the New Hampshire Statehouse in Concord in November. The state has played an important role in presidential primaries over the years, having picked 14 of the past 17 presidents. Charles Krupa/Associated Press

But the four-term U.S. representative marvels at what she called the historic number of undecided voters with just a week before the nation’s first primary is held here Feb. 11.

“I have never in my lifetime seen such a high number of undecided voters here,” said Kuster, 63, a Democrat.

As the Democratic candidates leave Iowa after Monday’s caucuses and descend on this small state, a recent survey by the University of New Hampshire found that nearly half of the electorate is undecided, with 31 percent firmly committed and 20 percent open to switching.

This indecision has heightened the potential impact of the Iowa vote, which historically influences the race in New Hampshire, depending on who finishes in the top tier. A Friday debate in New Hampshire could prove decisive.

Even the best-run campaign organization in New Hampshire will find it difficult to overcome a poor Iowa finish, according to Dante Scala, a professor of political science at the University of New Hampshire.

“You can build the boat,” Scala said, referring to a campaign organization. “But you win with the wind in its sails. If you are not the story out of Iowa, your sails can go limp anyway, and it doesn’t matter how well the boat is built.”

Don Brueggemann, manager of the Works Bakery Cafe on Concord’s Main Street, said Monday that many Democratic voters are “struggling” to make a decision and could be affected by the Iowa results. After meeting a number of candidates who have eaten meals at his shop, including former vice president Joe Biden, he decided only in the last few days to support Pete Buttigieg after talking with fellow voters at a house party.

“I’m pretty mainstream for the most part,” the 60-year-old said. “It’s really just trying to think of who is going to match up well against Mr. Trump. Initially, I was like, I don’t want to vote for anybody over 70 or anybody under 40.” Sen. Bernie Sanders, I-Vt., is 78, and Biden is 77. While he said “nothing Bernie says is untrue,” and “Biden has done some great things,” he decided to support the 38-year-old Buttigieg, former mayor of South Bend, Indiana, in hopes that he can unite Democrats.

Still, he said, he could change his mind if Buttigieg finished poorly in Iowa.

“If he didn’t rate in the top four, that would give me pause,” he said.

There have been questions for months about how important the New Hampshire primary will be because two of the leading candidates, Sanders and Sen. Elizabeth Warren, D-Mass., are from neighboring states, perhaps hurting the ability of other candidates to compete for a top finish.

But New Hampshire Secretary of State William Gardner, the longtime guardian of the first-primary status, insisted the state will be as important as ever. In the past 17 New Hampshire primaries, fourteen winners went on to be elected president and the other three who occupied the White House finished in second place here.

“No one has come in less than second in a New Hampshire presidential primary and gone on to be president,” Gardner said.

Yet by some measures, New Hampshire’s role has diminished. For example, there has been a historic lack of advertising by some of the leading candidates, many of whom have invested heavily in Iowa and other states.

Biden, for example, had spent $5,429 on television and radio advertising here as of mid-January, according to Advertising Analytics, which tracks such political spending. During the same period, Biden had spent $5 million in Iowa. (Advertising Analytics said Biden’s spending had increased here to $215,000 as of Monday.)

The airwaves have been dominated by Tom Steyer, the former hedge fund manager. The billionaire has spent $16 million on television and radio ads in New Hampshire as of Jan. 13, far more than any other candidate, according to Advertising Analytics. Steyer’s spending has not paid off; he has been in the low single digits in the polls.

The second-highest spender was Sanders, at $3.6 million.

Some of the top candidates are spending the least, in part because they have poured so many resources into Iowa. Warren spent $128,000 on television and radio advertising as of Jan. 13, according to Advertising Analytics.

Biden’s campaign has long sought to play down expectations here, given that Sanders and Warren are from neighboring states. But Biden himself recently delivered a conflicting message. While he stressed that he doesn’t need a victory here, he said on Jan. 26 on a local television station, WMUR, that “I think I will win New Hampshire.”

Ian Moskowitz, the director of Biden’s New Hampshire campaign, confirmed that Biden had spent $5,429 as of Jan. 13. Asked what that said about his competitiveness here, Moskowitz responded that “the person-to-person conversations are what matter here.” New Hampshire has a population of 1.36 million, making it one of the 10 smallest states.

While it is a New Hampshire political mantra that campaigning is personal, the number of Democratic primary voters is expected to exceed 250,000, according to Gardner. Of those, nearly 40 percent of the electorate are expected to be independents, and they may hold the key to victory. Independents are not allowed to vote in Iowa’s caucuses, so their presence here is perhaps the most significant political difference between the states.

The strength of independents was particularly evident here in 2016, when Sanders beat Hillary Clinton by a 52-48 margin among Democrats, but swamped her by 73-25 among independents, according to exit polls. Sanders won overall with 60 percent of the vote.

Kuster, who supports Buttigieg, noted that Sanders’s support is much lower than four years ago. Recent polls of this year’s much larger field show Sanders leading with support in the 20s. Kuster said that shows that many people who supported Sanders are open to other candidates.

Biden, meanwhile, faces challenges here that may be even greater than those he dealt with in Iowa. The relative lack of minorities, whose support is crucial to his bid, is once again a factor here. Whites make up 91 percent of Iowa and 93 percent in New Hampshire, according to Census Bureau figures.

A key difference between New Hampshire and Iowa is this state’s wealth. (The unemployment rates are nearly identically strong – 2.6 percent in New Hampshire and 2.7 percent in Iowa). Unlike Iowa’s farm-based economy, subject to the swings of trade wars and soybean prices, New Hampshire has thrived as a high-tech hub and attracts many wealthier residents seeking its low tax rates.

The median value of a home here is $253,000, compared with $142,000 in Iowa, and the percentage of people older than 25 with a college degree is 37 percent, compared with 28 percent in Iowa, according to Census figures.

Yet for all its economic might, New Hampshire’s working class is lagging, which helps explain the appeal of the message from a democratic socialist such as Sanders. Nearly 7 percent of people under 65 years old here do not have health insurance, compared with 5.6 percent in Iowa.

Another perceived Biden strength, his appeal to blue-collar voters, is being tested here by the emergence of several moderate candidates such as Sen. Amy Klobuchar, D-Minn., and Buttigieg. Both candidates have invested heavily in their organizations here to be prepared for the potential of capturing momentum from their hoped-for strong Iowa finish.

“We are well-positioned to use our organization here in New Hampshire to persuade undecideds and independents,” said Scott Merrick, Klobuchar’s state director.