AMNA NAWAZ: House Republican leaders continue to struggle to conduct the basic functions of government, hindered by a razor-thin majority and infighting within their ranks.

This Congress has witnessed failed floor votes, two extended battles for the speaker's gavel, and the booting of former Congressman George Santos late last year.

As Lisa Desjardins explains, the latest wrinkle will come tomorrow, when Santos' district gets its congressional voice back.

(CHEERING AND APPLAUSE) LISA DESJARDINS: At the base of Long Island, a race for Congress with a New York persona, fast, massive stakes, and quite a backstory; 73 days ago, House members ousted serial fabulist George Santos.

That empty seat has been the difference in some key votes... REP. MIKE JOHNSON (R-LA): The resolution is not adopted.

(CHEERING AND APPLAUSE) LISA DESJARDINS: ... including last week's attempt to impeach Homeland Security Secretary Alejandro Mayorkas, which failed in the House by one vote.

Democratic hopes in the race are pinned on Tom Suozzi messaging seriousness.

FMR.

REP. TOM SUOZZI (D-NY): This is not a game.

This is not about tweets.

This is not about press conferences.

This is about real people's lives.

LISA DESJARDINS: Suozzi is a moderate Democrat who held the seat for six years, before falling short in his 2022 bid for governor.

Facing him... MAZI PILIP (R), New York Congressional Candidate: You are a talker.

I am the person who will deliver.

When I promise, I will deliver.

LISA DESJARDINS: ... is Mazi Pilip, an Ethiopian-born Israeli-American who served in the Israeli Defense Forces and is a county lawmaker elected to office as a Republican, but still registered to vote as a Democrat.

GRANT LALLY, Publisher, The North Shore Leader: She sits and caucuses and votes with the Republicans.

LISA DESJARDINS: Grant Lally, publisher of The North Shore Leader, has a unique vantage point.

His small paper first exposed George Santos' lies and now is covering his replacement.

GRANT LALLY: It's a special election, and it's a nationally famous special election.

People are watching it.

The big issue here is migrants, migration, the border crisis, because there are tent cities now in this congressional district holding thousands of migrants.

LISA DESJARDINS: The months of migrant crisis in New Yorkers' turf has dominated the campaign, and it's why Lally's newspaper endorsed Pilip, though it endorsed Suozzi in past years.

GRANT LALLY: The immigration issue is so important and the migrant issue is such a crisis, particularly locally, that we felt that her election would send the right signal in dealing with it seriously.

LISA DESJARDINS: And she is signaling that she's in line with most House Republicans, including on Mayorkas.

MAZI PILIP: Yes, absolutely, I would vote to impeach.

Mayorkas, he failed to protect the American people.

He should not be there.

And this is why this election is so important.

We have to have a strong majority to start to do the right things.

LISA DESJARDINS: But same issue and a different local newspaper, Newsday, sees Suozzi as the solution, writing that he would work across the aisle to find real border solutions.

That's Suozzi's message, that he's tough, but not partisan on the border.

FMR.

REP. TOM SUOZZI: She says she's concerned about the border, but she opposes the bipartisan solution that would actually close the border.

LISA DESJARDINS: Meanwhile, both candidates tiptoe around their presumed tops of the ticket in November, President Joe Biden and former President Donald Trump.

Emily Ngo covers New York state politics for Politico.

EMILY NGO, Politico: A lot of local seats have flipped red since Joe Biden won this district in 2020.

Suozzi doesn't want to be closely affiliated with Joe Biden because he's so unpopular in the district.

LISA DESJARDINS: Pilip had praised Trump, but until this weekend wouldn't say she voted for him in 2020.

And when it comes to his legal problems...

QUESTION: Just so I'm clear, if he is convicted of a crime, you will not support him?

MAZI PILIP: I'm not going to support.

Nobody is above the law.

LISA DESJARDINS: The race has brought an avalanche of ads.

FMR.

REP. TOM SUOZZI: I'm Tom Suozzi, and I approve this message.

MAZI PILIP: I'm Mazi Pilip, and I approve this message.

LISA DESJARDINS: But as they play, an actual storm, a snowstorm, is brewing that could make early voting critical.

EMILY NGO: Normally, it favors Democrats, who like to turn out early, versus Republicans who come on Election Day, but both parties, both candidates really pushing their supporters to bank their votes and come out before the storm hits.

LISA DESJARDINS: New York Democrats are in the process of redrawing the state's congressional battle lines, presumably in their party's favor.

And this district's lines will be closely watched.

EMILY NGO: The path to the gavel in the House most likely runs through about half-a-dozen seats in New York state in the suburbs.

LISA DESJARDINS: Meaning, in Long Island, tomorrow, we have a race that could preview how suburbs will break this fall and also how the House will operate next week.

For the "PBS NewsHour," I'm Lisa Desjardins.