KOBYLIN-BORZYMY, Poland — The twin steeples of Saint Stanislaus, a hulking, red-brick Catholic church, are visible for miles across the corn fields and cow pastures of this conservative area of eastern Poland, a bastion of support for the country’s nationalist governing party.

That party is “conservative and Catholic, and people here are very attached to national traditions and the church,” said Dariusz Sikorski, the elected chief of a county that gave more than 90 percent of its vote to the party’s victorious candidate in a presidential election last year.

They are also deeply attached, however, to cash from the European Union. Taxpayers in the 27-nation bloc provided nearly $150 million to build a nearby highway and millions more to help pay for a children’s playground, water pumping stations, a sewage system, clean-energy projects and improvements to the local school.

With Poland now locked in a tumultuous struggle with Europe over the rule of law that has raised the possibility, albeit very small, of the country being forced to leave the bloc, the government in Warsaw is wrestling with tension between nationalist instincts suffused with religious faith and the reality of economic and political self-interest.

How that tension resolves itself will decide the outcome of the European Union’s biggest crisis since Britain voted to leave the bloc in a 2016 referendum.

Relations with Brussels, the seat of the bloc’s executive, have become so frayed that the ruling Law and Justice party and its supporters in Warsaw have tossed ever more incendiary verbal bombs, threatening to “set fire to Europe” and reviling the European Union as a bullying “colonial” force. The Polish prime minister has even talked of a ‘third world war.”

But places like Kobylin-Borzymy seem in no mood for a fight to the death. Poland has received more than $225 billion from the European Union since it joined in 2004. It is slated to get nearly that much again in grants and loans during the current budget ending in 2027, plus another $47 billion as part of Europe’s Covid recovery program.

As for claims by hard-line nationalists in Warsaw that the European Union is an “occupier” akin to the Soviet Union and Nazi Germany, “nobody really believes that,” said Mr. Sikorski, who presides over a local council whose 15 elected members all support Law and Justice.

Many farmers in the area, the backbone of the local economy and a deep well of votes for Law and Justice, would have trouble staying afloat without subsidies from Brussels, he said. “Almost everyone here benefits from the E.U.,” he said. Leaving it, he added, “is not a realistic option.”

But such a departure, a version of Britain’s Brexit known as Polexit, has suddenly become a possibility after Poland’s constitutional tribunal ruled this month that the country’s national laws were superior to European law. Senior officials in Brussels and European politicians have denounced the ruling as an intolerable threat to the foundations of the union that cannot stand if Poland wants to stay a member.

Europe’s clash with the biggest of eight formerly Communist nations that joined the bloc in 2004 has been building for years over media freedom, L.G.B.T.Q. rights, coal mining and other issues. But the crisis threatened to boil over this month with the court ruling.

“You are sleepwalking toward an exit from the European Union,” a German member of the European Parliament told the Polish prime minister, Mateusz Morawiecki, during a heated debate on Poland last week at a session of the legislature in Strasbourg, France. The E.U., the German liberal, Moritz Körner, said, “is not a kind of self-service store. If you do not want to observe European law, you cannot remain a member.”

The ruling party’s loyal supporters in Kobylin-Borzymy mostly dismiss talk of Poland leaving the E.U. as an idle threat cooked up by foreign and Polish liberals, a view promoted enthusiastically over the past week by state television.

At least they hope it is.

Leszek Mezynski, a retired dairy farmer and deputy head of the regional council, said the conservative district wanted to keep out migrants and liberal ideas like gay marriage to avoid “civilizational suicide.” But it is more concerned, he said, about losing the economic benefits that flow from European farm subsidies, funding for new roads and other large dollops of cash.

Polexit “is not something anyone out here really wants,” Mr. Mezynski said.

Until Britain voted to leave in a 2016 referendum, however, Brexit was not something many Britons seemed to want either, or expected to happen.

Unlike Britain, where hostility to the European Union featured as a powerful force in domestic politics long before the 2016 vote, Poland has never had a significant lobby pushing for it to withdraw. In contrast to Britain before its departure, Poland gets far more money out of the bloc’s pot than it puts in.

A 2004 Polish referendum on joining the union passed with 77 percent of the vote and support for staying in it has since risen to nearly 90 percent, according to opinion polls.

Warnings that Poland is jeopardizing its membership have left the ruling party vulnerable to accusations by the opposition leader, Donald Tusk, that the government, for all its patriotic bluster, has effectively aligned itself with Moscow by undermining European unity. That is a potent charge in a country with an abiding fear of Russia.

Last week, Mr. Tusk, a former Polish prime minister and, until 2019, president of the European Council in Brussels, drew tens of thousands of people chanting “we are staying” to a noisy pro-Europe protest in central Warsaw. At a separate rally in the northern city of Gdansk, the former Solidarity trade union leader Lech Walesa, who won the Nobel Peace Prize for leading opposition to Poland’s Communist regime in the 1980s, denounced the government for putting Poland’s membership in the bloc at risk.

Polish cities, however, have long opposed Law and Justice. Far more worrying to the ruling party is the unease felt in its rural base.

The entrance hall to the primary school in Kobylin-Borzymy, named after a 16th-century Polish Jesuit priest celebrated for his patriotism, is adorned with crucifixes and a tribute to the Polish-born Pope John Paul II. The school, too, has been helped by money from Brussels, which provided aid for new insulation and a preschool.

Despite declarations by Prime Minister Morawiecki that Poland is a “proud country” that will never submit to E.U. financial pressure, such pressure has sometimes worked, even in the party’s heartland.

Scores of Polish towns dominated by Law and Justice caused outrage across Europe in 2019 by declaring themselves “L.G.B.T.-free” zones. But one by one, threatened with cuts in European funding, some have since quietly retreated.

And Mr. Morawiecki, shortly after vowing last week to never surrender in a defiant speech to the European Parliament, opened a clear path to a partial surrender. He told legislators that his government would scrap a disciplinary chamber for judges that Europe’s top court and its most senior officials see as compromising the independence of the Polish judiciary. They have repeatedly demanded that Poland dismantle it, and reverse other changes to the judicial system introduced by the ruling party.

Ultimate decision-making power in Warsaw, however, rests not with the prime minister, but with Jaroslaw Kaczynski, 72, the ruling party’s deeply conservative and unpredictable leader.

Mr. Kaczynski, a fervent Catholic and lifelong bachelor, is reviled by liberals as a reactionary oddball. But he has an uncanny political sense that has made him Poland’s dominant figure, though it is now being tested by Warsaw’s clash with Brussels.

He has to worry about alienating voters who depend on European money as elections scheduled for 2023 approach. At the same time, he is struggling to hold together a fragile coalition government that depends on a far-right faction led by Justice Minister Zbigniew Ziobro, the architect of changes to the judiciary now at the heart of the rift with Europe.

In an interview last week with a conservative weekly magazine, Sieci, Mr. Kaczynski dismissed the possibility of “Polexit” as “complete nonsense” invented by his opponents. But he also made clear that he does not want an early election, something that will be hard to avoid unless he appeases Mr. Ziobro and fellow Euroskeptics.

While there is no sign yet of any mass defection by his supporters, some voters are having second thoughts.

Piotr Perkowski, a 43-year-old farmer who gets European subsidies and used to vote for Law and Justice, said, “I definitely won’t vote for them now.” The government took money from the European Union to build a new water-pumping system, he said, but did not connect his house to it, leaving his family without running water. Law and Justice, he said, “made too many promises it did not keep.”

But Law and Justice, aided by state television, has convinced many people in Kobylin-Borzymy that the opposition, not the government, is to blame for stirring doubts about Poland’s membership in the bloc by airing the country’s domestic quarrels in front of foreigners.

“People should settle their disputes at home and not shout so their neighbors can hear,” said Kazimierz Kloskowski, whose family farm produces corn and wheat. All the same, as a recipient of cash subsidies from Europe, he’s not entirely convinced that escalating tension with Brussels is a good idea.

“There is no other option for us except Europe,” he said. “The only alternative to Brussels is Moscow. And we already know what this is like.”

Anatol Magdziarz contributed reporting from Warsaw, and Monika Pronczuk from Brussels.