On the tarmac on Monday, Ms. Tenney and her son, a Marine captain, were the first to greet Mr. Trump and Air Force One as he arrived in nearby Rome, N.Y., as the crowd of roughly 50 people rotated between shouts of “Build that wall!” “USA! USA!” and “Trump! Trump!”

As the president signed hats and shook hands with some in the crowd, Ms. Tenney stood nearby with her outstretched arm, filming it all on her cellphone.

Ms. Tenney’s district, which stretches from Binghamton to Lake Ontario in Central New York, is one of the most fought-over seats in America, with more than $1.6 million in “super PAC” money already pouring into the contest, more than any other New York race.

Ms. Tenney, who is in her first term, narrowly won a three-way contest with 46.5 percent of the vote in 2016, and her re-election is seen as a tossup, as Democrats recruited a more centrist challenger, Assemblyman Anthony Brindisi. Both Mr. Brindisi — whom Mr. Trump characterized as a “total puppet of Nancy Pelosi” — and Ms. Tenney have raised nearly $2 million.

Outside the hotel, about 100 Trump supporters stood across the street from roughly 400 protesters, several of whom spoke out against the president’s policies on immigrants and refugees because of Utica’s large refugee population. The United Nations named Utica “the town that loves refugees,” as it has resettled more than 16,000 refugees over the past three decades. Utica has a population of just over 60,000.

The protesters also took issue with the cost of attending the fund-raiser. Even some Republicans were perplexed that Mr. Trump — who can draw massive crowds at a rally or massive checks from deep-pocketed donors — would choose to headline a fund-raiser in Utica, a city of 60,000 hardly known for its financial might.

Tickets to get in to Monday’s event started at $1,000. For $15,000, hosts received access to an exclusive round table and reception with Mr. Trump, plus a photo.