MANCHESTER, N.H. — When Senator 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, Ms. 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 Ms. Ayotte, a 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 Obama in both 2008 and 2012, Ms. 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, Ms. 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 Ms. 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.