A new survey from Siena College finds that Congressman Tom Suozzi’s 4 percentage point lead over a county legislator, Mazi Pilip, is within the survey’s margin of error as the candidates brawl over border policy and immigration in a competitive race.

The poll, conducted by Siena College, found that Mr. Suozzi leads Ms. Pilip 48 percent to 44 percent in the race for the seat left open by the ouster of a disgraced congressman, George Santos. The survey of 694 likely special election voters had a margin of error of plus or minus 4.2 points.

“While both candidates have nearly breakeven favorability ratings, Suozzi is seen by voters as likely to do a better job on protecting democracy, addressing the issue of abortion, determining aid to Ukraine and making Congress work more effectively,” a pollster, Don Levy, said in a memo accompanying the results.

Mr. Levy added that Ms. Pilip “is viewed as better on addressing the influx of migrants and by a slim margin on establishing American policy towards the Israel-Hamas war.”

Mr. Suozzi’s advantage appears to have held steady since mid-January, when an Emerson College survey found that he held a 4-point lead over Ms. Pilip.

In the race, the situation at the southern border — which has bled into nearby New York City due to migrants being bussed to New York by the Texas governor, overwhelming city services — has taken a front-row seat among issues for candidates of both parties, with Mr. Suozzi endorsing the recent bipartisan Senate deal and Ms. Pilip rejecting the legislation.

Mr. Suozzi has made border messaging a central part of the final push in his campaign in an attempt to make up ground on an issue where Ms. Pilip has an advantage.

In a statement Wednesday, Mr. Suozzi attacked Ms. Pilip, claiming that after “saying absolutely nothing of substance for the past two months, Pilip is now against the bipartisan compromise that offers our best chance at securing the border in 40 years.”

“She’s endorsing chaos at the border because she believes it will help her and Donald Trump politically,” Mr. Suozzi said.

The Siena College survey found that Ms. Pilip is preferred on the issue of border security ahead of Mr. Suozzi, with 49 percent of respondents backing Ms. Pilip to Mr. Suozzi’s 40 percent.

At the same time, the National Republican Congressional Committee has been attempting to associate Mr. Suozzi closely with President Biden.

“Tom Suozzi can try his best to hide his friendship with Joe Biden, but the truth is he voted with him 100 percent of the time while in Congress,” an NRCC spokeswoman, Savanah Viar, said in a statement. “Joe Biden and Tom Suozzi are two sides of the same, rusty, unwanted coin.”

Despite Mr. Suozzi’s lead, respondents to the survey prefer President Trump over Mr. Biden, 47 percent to 42 percent. Yet both men are also viewed overwhelmingly negatively, with Mr. Trump having a negative 15-point net approval rating, and Mr. Biden having a negative 18-point net approval rating.

The special election on February 13 has attracted attention from both parties not only for its potential to build momentum going into the 2024 elections, but for its more immediate implications for governing.

Earlier this week, House Republicans failed to pass a measure to impeach the secretary of homeland security, Alejandro Mayorkas, due to their slim majority, some absences in the House, and a handful of GOP representatives opposing the measure.

If Democrats are able to win the special election at New York’s Third, it would put further strain on the GOP coalition and potentially give Democrats the opportunity to block another impeachment measure against Mr. Mayorkas or Mr. Biden.

The race, despite being a special election that typically has low turnout, will also serve as a potentially useful datum point in gauging the sentiment of voters in the New York City suburbs, an area that proved to be decisive in deciding control of Congress in the 2022 midterms.

The Cook Political Report rates New York’s Third District as a “toss-up.”