The candidates vying to replace George Santos in a special House election squared off on Thursday in an exceedingly bitter debate, tangling over the roots of New York City’s migrant crisis, abortion rights and, at one point, the definition of “assault weapon.”

The face-off on Long Island was the only chance for voters to see the candidates debate, and each sought to smear the other at close range. Mazi Pilip, the Republican nominee, claimed that her opponent, Tom Suozzi, “opened the border.” He called her wholly unprepared for Congress.

The Feb. 13 election is considered a tossup. A victory by Mr. Suozzi would narrow Republicans’ paper-thin House majority at a time when they are already struggling to govern. If he loses, it could signal trouble for Democrats ahead of November’s elections.

Here are five takeaways from the debate, hosted by News 12.

The migrant crisis is dominating the race.

New York is almost 2,000 miles from the U.S.-Mexico border, but it is clear the race has become a referendum on the influx of migrants trying to get across it. The only question is who will take the blame in the eyes of frustrated voters.

Ms. Pilip, a Nassau County legislator who immigrated from Israel, offered spare details about her own prescriptions to secure the border (she supports a wall and more border agents). But she repeatedly accused Mr. Suozzi, a moderate former three-term congressman, of siding with President Biden and far-left members of the House “squad” to encourage illegal immigration.

“Tom Suozzi opened the border. Tom Suozzi funded the sanctuary city. Tom Suozzi kicked I.C.E. from Nassau County,” she said. Addressing Mr. Suozzi, she added, “This is absolutely you; you have to own it.”

Mr. Suozzi called the accusations “absurd,” explaining that he supported Immigration and Customs Enforcement and had only moved against the group in 2007 after rogue agents pulled guns on Nassau County police officers.

“For you to suggest I’m a member of the squad is about as believable as you being a member of George Santos’s volleyball team,” he quipped.

More notable were Mr. Suozzi’s attempts to go on the offensive on an issue that typically favors Republicans. He pitched himself as a pragmatic deal-maker and sharply criticized Ms. Pilip for her opposition to a bipartisan Senate bill that would have clamped down on asylum claims and closed the border if there were too many attempted crossings.

“Her opposition will result in the border staying open and more migrants coming to New York,” he said.

Ms. Pilip avoided questions on abortion and assault weapons.

Facing a deluge of ads attacking her position on abortion rights, Ms. Pilip said she wanted to set the record straight. Her answers did anything but.

Ms. Pilip said she was “pro-life” and the proud mother of seven children. But, she added, “I’m not going to force my own beliefs to any woman, therefore I’m not going to support national abortion ban.”

Yet when Mr. Suozzi tried to elicit more specific stances about restoring Roe v. Wade or how she would vote on potential restrictions that fall short of a national ban, the Republican pushed back. She accused Mr. Suozzi of trying to tell a woman what to think about her own body and of distorting her record.

“How dare you lie like this,” she said. But she never answered his question, or follow-ups from a moderator.

A similar pattern played out when an audience member asked whether the candidates would support a ban on the type of assault weapons frequently used in mass shootings.

Mr. Suozzi said he would support a ban, and proudly reminded viewers of his “F” rating from the National Rifle Association. Ms. Pilip answered a question that was not asked.

“I don’t see any reason why the average American or individual would have more powerful weapon than our cops,” she said. “Therefore, I am not going to support assault automatic weapons.”

But automatic weapons are already illegal for civilians, as Mr. Suozzi pointed out. And when he asked again whether she supported banning semiautomatic weapons like AR-15s, Ms. Pilip did not say.

Experience or a fresh face?

Mr. Suozzi, 61, once ran a campaign for governor with the slogan, “I can do it because I’ve done it.” He offered voters the same message Thursday night, showing off his fluency on thorny tax issues and foreign policy.

Ms. Pilip, who, at 44, is serving her second term on the part-time Nassau County Legislature, presented herself as a comparatively fresh face. “I’m not a typical politician who’s so good at talking,” she said.

Both approaches are, in their own ways, aimed at winning over moderate suburban voters turned off by hyperpartisan politics. But their drawbacks were also on full display.

Ms. Pilip deployed a two-word pejorative — career politician — to describe her opponent and drew from his long record on immigration and taxes to attack him.

She, in turn, had moments where she looked particularly unseasoned for a congressional candidate in a major race. Pressed to explain how she would reinstate the full state and local tax deduction, a major issue for homeowners, Ms. Pilip suggested that voters should just trust her.

“When I want something, I will deliver,” she said.

The race is very, very close.

With only five days before Election Day and early voting underway, there was little reason to believe the exchanges had enough force to alter the race’s trajectory as it barrels toward an exceedingly close finish.

A pair of polls released on Thursday showed Mr. Suozzi with a slight lead, though both results were within the surveys’ margin of error. A Siena College poll conducted for Newsday had Mr. Suozzi leading Ms. Pilip, 48 percent to 44 percent, among likely voters. Another survey from Emerson College for WPIX-TV found him up 50 percent to 47 percent.