If you want to be the president, you should probably win Wisconsin.

And if you are a Democrat, there is a proven way to do that: Run up the numbers in Dane County, the fast-growing and deeply progressive swath of the state that contains Madison and the behemoth public university that carries the state’s name.

President Biden’s trip on Monday to a technical college in Madison, where he announced a new plan to help pay off student loans, seemed to be part of an effort to build excitement around his re-election bid in a college town that has been a bright spot for Democrats, one seen as crucial to his victory in the state in 2020 and vital to his chances in November.

“My district,” said State Senator Kelda Roys, a Democrat who represents much of Madison, “could potentially decide the fate of the free world.”

But this year, amid signs of an enthusiasm gap among young voters and widespread anger on college campuses over the administration’s handling of Israel’s war in Gaza, college towns are emerging as a more complex battleground for Democrats. So I decided to head to Madison myself.

“I’m definitely a little bit nervous,” said Megan Eisenstein, the communications director of the College Democrats group at Lawrence University, who had traveled from her campus in Appleton, Wis., to Madison over the weekend for the statewide College Democrats convention.

“I think right now,” she added, “the hardest thing is to make young people excited about Joe Biden.”

The uninstructed vote

Last week, when Wisconsin voters went to the polls in snow and rain for the now-very-much-effectively-over presidential primaries, nearly 50,000 people cast “uninstructed” votes on the Democratic side — meaning 8.3 percent of the state’s Democratic primary voters seemingly decided to use their ballots to protest the Biden administration’s support for Israel’s war in Gaza.

That wasn’t enough to net the “uninstructed” voters any delegates to this summer’s Democratic National Convention, as “uncommitted” voters did in Michigan, where the protest movement was born.

But it was enough to send a signal about voters’ discontent with Biden — particularly in a state that he won by just 20,682 votes in 2020. (There was something of a protest vote on the Republican side too, with Nikki Haley, a candidate who has dropped out of the race, earning more than 75,000 votes.)

In Madison, almost a third of Democratic primary voters in wards on or near the university’s campus voted “uninstructed,” according to an analysis by The Daily Cardinal, the University of Wisconsin-Madison’s independent student newspaper.

“This is more than just nit-picking, like, ‘I’d prefer if it was the other way,’” said Dahlia Saba, a student organizer with Listen to Wisconsin, the group that led the push for the “uninstructed” vote. “This is deep betrayal, and deep anger.”

State Representative Francesca Hong, a Democrat who endorsed the campaign for the “uninstructed” vote, said there is a risk that Biden could underperform here in November.

“I think there are people who say now that they will never vote for this president,” Hong said, although she believes there is still time for Biden to mobilize those voters if his administration shifts its policy regarding the war.

Democrats take notice

On Sunday afternoon, in a plenary hall at the business school at the University of Wisconsin-Madison, the College Democrats of Wisconsin were finishing up their convention business in front of a sunny slogan: Blue Skies Ahead!

The student Democrats here are hugely proud of how they turned out in droves in 2020, in the midterms and last year’s state Supreme Court election, which flipped the court to liberal control. They see themselves as tipping-point voters in a tipping-point state.

But as they packed up their blue plastic tablecloths and empty cups of iced coffee, some of the activists expressed a current of worry, too.

“With Joe Biden seeing the results in Michigan and Minnesota” Matthew Lehner, the newly elected chair of the group, said, referring to the uncommitted votes in both of those states, “it is certainly my hope, and it’s certainly my desire that they listen to folks.”

Ben Wikler, the chair of the Democratic Party of Wisconsin, said the state’s races were too close not to pay attention to anything that could shape turnout.

“It’s absolutely the case that turnout in any set of wards in Wisconsin can tip not just Wisconsin, but the entire presidential race,” Wikler said.

But he takes comfort in the fact that young people in cities like Madison chose to express their disappointment in Biden by going to the polls — not by staying home.

“This fall,” he said, “we’ll be working to to ensure all that energy is channeled into ensuring we defeat Trump again.”

The enthusiasm gap

Every set of college voters is different, from election to election, said John Della Volpe, the director of polling at the Institute of Politics at the Harvard Kennedy School and an expert on the youth vote.

“This generation seems to be voicing concern over Gaza, and also voicing concern about why all of this matters, why voting” matters, Della Volpe said. “That’s the biggest concern.”

A poll conducted by Della Volpe late last year found that young voters appeared less likely to vote in 2024 than in 2020, and a Times poll conducted this year found that young voters were the age group least likely to feel hopeful or excited about the election.

The Biden campaign has a national organizing program aimed squarely at young voters and is working with youth voting groups to make over 155 million “direct voter contacts.” Still, a lack of enthusiasm was palpable on campus in Madison. Sophie Filipczak, a freshman, grimaced when she was asked about the election over coffee in the student union.

“We haven’t had those really cool candidates,” said Filipczak, a Democrat, who said she was planning to vote for Biden but wished she were more excited. “It’s the rich, it’s the old — that’s just kind of how it’s been.”

Her friend Calissa Schumacher, an independent voter, said she planned to back an independent candidate in the fall because she did not like either major-party option.

“I just can’t stand for either Trump or Biden,” she said. If it came down a choice between those two and the independent candidate Robert F. Kennedy Jr., she said, she would vote for Kennedy.

The Biden campaign says it is working hard to communicate the president’s accomplishments across campuses like this one — but neither Filipczak or Schumacher planned to pay much attention to the official visit in their own backyard, where he was doing just that.

“I can’t say I’m, like, super gung-ho about going to see him,” Filipczak said.