MANCHESTER, N.H. >> When Sen. Kelly Ayotte is in Washington, she plows through the halls of the Capitol, her face pinched into an expression somewhere between suspicion and agitation, a human tuning fork of intensity.

But from the moment the New Hampshire Republican rolls her carry-on bag to the airport gate for her flight back home, Ayotte’s face softens, her gaze broadens and she chats with half her fellow passengers, all of whom she seems to know — lobbyists, college students, someone who has noticed her daughter’s basketball game has improved.

She may not always telegraph it, but the freshman senator is locked in a herculean battle with the state’s popular Democratic governor, Maggie Hassan. As one of five Senate Republicans running for re-election in states that supported President Barack Obama in both 2008 and 2012, Ayotte is seen as particularly vulnerable this November, and is a major reason national Democrats, now on the short end of a 54-46 Republican majority, are optimistic about taking back the Senate.

Six years ago, Ayotte was part of a Republican wave that swept Democrats out of power in blue states like Illinois and Wisconsin, as well as swing states like New Hampshire. For Ayotte and other Republicans from that class, 2016 was always going to be a difficult year to run for re-election because more Democrats vote in presidential years. But with the possibility that Donald J. Trump, the most divisive Republican presidential candidate in a generation, will be at the top of the ticket, the party’s task may be all the more arduous.

“They have to find a way to keep Trump voters excited, and appeal to those who are offended by him,” said Nathan Gonzales, editor of The Rothenberg & Gonzales Political Report. “That is the tension they have to navigate.”

Nowhere is that tension more apparent than in New Hampshire, a moderate state that also gave Trump one of his most critical victories in its presidential primary last month.

“New Hampshire is one of the most competitive races in the Senate,” Gonzales said. “If the cycle turns into a catastrophe for Republicans, New Hampshire will be one of the first states to fall.”

Ayotte, like most of her Republican colleagues, stands with Sen. Mitch McConnell of Kentucky, the majority leader, in opposing a confirmation vote on a Supreme Court nominee, in refusing to reject Trump should he become the party’s nominee and in opposing Obama. But on issues that appeal to moderate voters — drug programs for addicts, clean power plants and the so-called Gang of Eight immigration bill — Ayotte has often sided with Democrats. And that is likely to be a familiar strategy for some of her fellow Senate Republicans this year.

“With the potential for a polarizing nominee like Trump or Cruz at the top of the ticket, it will be more important than ever for Republican Senate candidates to cement their own identity and distance themselves when necessary,” said Brian Walsh, a longtime Senate campaign aide and Republican consultant, referring also to Sen. Ted Cruz of Texas. “Senators in both parties have been successful in doing that in recent years, but you need to run hard and run your own race because the top of the ticket inevitably dominates the broader national political environment.”

Other Republicans from the class of 2010 — Sens. Rob Portman of Ohio, Patrick J. Toomey of Pennsylvania and Mark S. Kirk of Illinois — have also found issues that could distinguish them from more conservative members of their party (for Portman, programs for drug addicts; for Toomey, gun safety; for Kirk, agreeing to hearings for Judge Merrick B. Garland, Obama’s Supreme Court nominee). Sen. Ron Johnson of Wisconsin is an exception; he has not strayed far from his Tea Party roots in his campaign.

Nationally, Ayotte had a similar image as a conservative, augmented by Sarah Palin’s anointment of her as a fellow “mama grizzly” during the 2010 campaign, her alliance with Sens. John McCain of Arizona and Lindsey Graham of South Carolina on interventionist foreign policy views, and her numerous votes to defund Planned Parenthood.

But in her home state, Ayotte, 47, has a different image.

“The perception outside of here that Kelly Ayotte is part of the Tea Party was actually false,” said Andrew E. Smith, a political scientist and pollster at the University of New Hampshire.

“She is pretty much Judd Gregg in a skirt,” he said, referring to the moderate Republican senator and former New Hampshire governor who preceded Ayotte.

Hassan, her opponent, is also a lawyer, and entered politics in 1999 when Gov. Jeanne Shaheen, now a Democratic senator, appointed her to a state education commission. One of her children has cerebral palsy, and she has said her quest to have him educated in a traditional school inspired her to seek elected office.

Shaheen, her mentor, describes her as someone who “has shown she can work across the aisle.” And just as Ayotte has tried lately to play up her spirit of bipartisanship, Hassan broke with her party shortly after announcing her candidacy this winter when she said the federal government had to put in place a better screening process for Syrian refugees before she would allow any in New Hampshire.

But more recently her message seems borrowed from Sen. Bernie Sanders of Vermont, the winner over Hillary Clinton in New Hampshire’s Democratic presidential primary.

Trump and Sanders voters share “a pervasive feeling that the system is truly rigged,” she said in an interview in her office in Concord, N.H. “People are very frustrated and angry, and have this sense that no matter how hard you work, you can’t get ahead and stay ahead.”

Drawing a contrast with Ayotte, she said, “We’ve tried to lower costs of higher education; I froze tuition” at the public universities. “While we were working so hard to do that, my opponent voted for deep cuts to Pell grants. She protected tax breaks for big oil. She voted to defund Planned Parenthood six times.”

The state’s economy is doing well — the unemployment rate last month was 2.7 percent. A bigger regional issue is drugs. Almost 50 percent of state residents know someone who has been affected by opioid abuse, according to a WMUR/University of New Hampshire poll.

Both Hassan, who managed to expand the state’s Medicaid program under the Affordable Care Act, even though Republicans control the legislature, and Ayotte, who helped push through a bill this month to address the crisis nationwide, have tried to raise their profiles on the issue.

Because New Hampshire is a small state, elected officials and political rivals like Ayotte and Hassan find themselves at the same events.

“Hi, everyone,” Ayotte said breezily, strolling from table to table at a St. Patrick’s Day charity dinner this month in Manchester, as Hassan stood several feet away with a group of aides. The senator settled down at a table just as the governor rose to make a mildly awkward joke out of how Ayotte’s plane might have been late, but a pilot change could not be made because “it’s up to the American people to decide” how to replace him.

The joke, in reference to Ayotte’s insistence on not voting on a Supreme Court replacement for Justice Antonin Scalia, drew nervous laughter and some boos, but underscored what Democrats hope is a high card in a contentious battle.

“I try to really focus on my state,” Ayotte said. “People know both of us. She has been the governor, and I have been the senator. And, of course, the presidential election is an important one, but people here are going to be able to distinguish and look at our race on its own.”

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