As his campaign manager tells it, U.S. Representative Tim Bishop of Southampton might not be in the fight of his life, but he’s certainly waging the liveliest reelection campaign of his career, as he faces both a tide of anger directed at Washington, D.C., and a deep-pocketed opponent, Randy Altschuler, who is aiming to capitalize on it.

Lisa Wieber, Mr. Bishop’s campaign manager, said the incumbent congressman has amped up his fundraising and outreach efforts this year in a push to hold on to the seat he has occupied since 2002. Although Mr. Bishop, a Democrat, handily dispatched his Republican opponents in 2004, 2006 and 2008, this year he is running in an atmosphere of hostility toward incumbents, who usually command a heavy advantage in U.S. House of Representatives races.

“I think this is the most serious climate,” Ms. Wieber said. “I don’t think Randy Altschuler himself is a threat. I think the climate is the concern.”

Meanwhile, Mr. Altschuler, a business owner from St. James, is looking to appeal to a contingent of voters that is dissatisfied with the administration of President Barack Obama and the Democrat-controlled Congress, including members of the Tea Party.

“I think those voters have been courted throughout this election by Randy talking about cutting taxes, cutting spending and cutting the deficit,” said Mr. Altschuler’s spokesman, Rob Ryan. “Those are three of their top issues, and I think those are the top issues of most voters this election year.”

Mr. Ryan said he sees signs of concern, even “desperation,” in some of Mr. Bishop’s advertisements. The congressman, he said, has shied away from identifying himself as an incumbent or a Democrat, or even mentioning that he is running for his fifth term.

“Anyone who is an incumbent is trying, I think, to run away from the incumbency, especially if you have the word ‘Democrat’ next to your name,” Mr. Ryan said. In response to that charge, Ms. Wieber wrote in an e-mail that Mr. Bishop is running on his record, as he has in the past.

There are reasons to believe Mr. Bishop is not as vulnerable as his opponent hopes. Albert Cover, a political science professor at Stony Brook University who specializes in congressional elections, said talk of a national anti-incumbent revolution is likely exaggerated. The U.S. House of Representatives, which historically returns an overwhelming number of its incumbents each election, may see enough of a turnover this year to put the Republicans in the majority—but even in that “worst-case scenario,” Mr. Cover said, most Democrats would still win reelection.

A poll conducted by Siena Research Institute earlier this month and released last Wednesday shows Mr. Bishop with a discernible lead over Mr. Altschuler—he is favored by 51 percent of likely voters to Mr. Altschuler’s 39 percent.

The poll surveyed 615 likely voters over the phone between October 6 and 11, picking them from a batch of 804 registered voters in the 1st Congressional District, which stretches from Montauk to Stony Brook. Something of an anti-incumbent sentiment may be palpable in the results: 48 percent of respondents said they were inclined to reelect Mr. Bishop, while 43 percent said they “prefer someone else.” But respondents generally said they viewed Mr. Altschuler unfavorably—44 percent to 33 percent—while viewing Mr. Bishop favorably—50 percent to 41 percent. Respondents also rated Mr. Bishop higher on every campaign issue, including jobs, health care, taxes and education.

Still, the reason Siena decided to study the race in the first place is because the 1st Congressional District is considered a political battleground this year, according to Steven Greenberg, a pollster for the institute. “I mean, I think it’s still viewed by both sides as a district that’s important to hold on to or to try and pick up, and Republicans still believe, I think, that they have an opportunity to win that district, and the Democrats are incredibly concerned about holding onto this district,” he said.

Mr. Ryan said he didn’t take the results at face value, because, he said, Siena has gotten polls wrong in the past. “We question the veracity of that poll,” he said. “Their past track record has not been great. We think it’s a very, very close race, and if I was Congressman Bishop, I would be very concerned right now.”

The race is by far the most expensive one of Mr. Bishop’s career, in part because he has had to keep pace with Mr. Altschuler, who has pumped $2 million of his own money into the race as of September 30. The challenger also has raised an additional $1 million from individuals, $79,000 from political action committees, $5,000 from his party and $80,000 from other sources, for a total of about $3.2 million.

Mr. Bishop has been hard-pressed to keep up. Ms. Wieber pointed out that his fundraising totals are the highest of his political career—he has raised $1.3 million from individuals, $860,000 from political action committees and $3,600 from other sources, for a total of about $2.2 million. But thanks to Mr. Altschuler’s personal contribution to his own campaign, that’s about $1 million less than Mr. Bishop’s opponent has to spend. The incumbent has received almost no money from his party and has not contributed any of his own funds to the race.