IDOMENI, Greece — On a recent weekday, 40 buses jammed into the parking lot of a gas station near the Macedonian border, carrying thousands of refugees who had survived a wintry sea crossing from Turkey.

Now they were approaching ground zero in the intensifying debate over how to curb the unceasing stream of men, women, and children from war-ravaged and poor nations in the Middle East and Africa to the safety and prosperity of Europe.

After trying and largely failing to persuade Turkey to stem the flow, Europe has reached a critical point in the migrant crisis. With few options left short of halting the war in Syria, much of the continent is coalescing around proposals that would harden the border with Macedonia and effectively turn Greece into a giant processing center for migrants.

At the border crossing here — one of the busiest gateways for migrants on the path north and the site of occasional violence between authorities and frustrated migrants — Greece has played that filtering role to some degree for months. In theory, Greece is allowing only Syrians, Iraqis, and Afghans to continue toward their preferred destinations in Germany and Austria.

The rest — from places like Iran, Morocco, Eritrea, Libya, Somalia, and Congo — are supposed to be sent to camps in Athens, where they can be deported or apply for asylum in Greece, whose economic troubles would make it an unattractive new home to most migrants even if they were accepted.

But other European nations say Greece is not doing enough to enforce the border and, with the number of refugees expected to surge again as the weather improves, the pressure for a new approach is escalating rapidly.

Exasperated with what they claim is a Greek policy of waving people through to the rest of Europe, officials in the European Union are talking about temporarily expelling Greece from the bloc’s passport-free internal travel zone, known as the Schengen area.

The European Commission president, Jean-Claude Juncker, endorsed a separate idea to send police from member states to Macedonia, which is not part of the EU, to buffer its side of the border with Greece. One Belgian minister even called for refugee camps for 300,000 to be built in Greece.

Greek officials have reacted angrily to the proposals. They say the plans would fail to deter migrants from heading to Europe in the first place and would stigmatize Greece — already under heavy EU oversight as it relies on international bailout funds — for a crisis exacerbated by other countries.

“The climate has changed from the welcoming politics of Merkel to one of fear and panic,’’ Nikos Xydakis, Greece’s foreign minister for European affairs, said, referring to Chancellor Angela Merkel’s decision last summer to open Germany’s doors to refugees. “If they want to raise a new Iron Curtain, we will not be the ones to blame.’’

If border controls are imposed on Greece, Xydakis said, “the flow will stop at the Greek sea, because people won’t want to be trapped in a black box in Greece. But migrants will just find other ways to get into Europe, even if they have to go through the Arctic Circle.’’

The EU last week proposed allowing countries to suspend the Schengen agreement for up to two years, a move that could push the system toward collapse and damage economies when Europe needs more resources to deal with the migrants. Several member countries, including Germany, Sweden, Hungary, and Austria, have temporarily reinstated border checks.

European officials blame Greece for creating a “domino’’ of tightened borders along the path to Germany.

In Macedonia, officials say that Greece must adequately distinguish refugees from migrants who have no claim to asylum, or many could get stuck in Macedonia if Serbia, its northern neighbor, rejects them.

“Then we will be the place where tents will be installed, and we’d become a huge refugee camp under open skies,’’ said Nikola Poposki, Macedonia’s foreign affairs minister. “We will do everything necessary to avoid that.’’

Here in Idomeni, at the official migrant camp abutting the checkpoint between Greece and Macedonia, Greek officers scrutinized the papers of hundreds of bedraggled refugees as they waited to cross an opening in a new 12.5-mile razor-wire fence now separating the two countries.

Although the migrant flow slowed in the winter, the numbers are higher than ever for this time of year. In January alone more than 45,000 migrants arrived at Greek islands from Turkey, a twentyfold increase from a year ago, despite a pledge of 3 billion euros in aid from the EU to Turkey in return for efforts to reduce the migrant flow.

Greek officials say they have improved critical efforts, like fingerprinting arrivals, stepping up sea patrols and upgrading registration facilities for migrants on the Greek islands.

In the meantime, the situation in Idomeni is but a taste of what Greece could look like if Europe decides to suspend Greece from the Schengen area or seal the border with Macedonia.

When Macedonia shut the border with no warning for a day last week, migrants piled behind the razor wire fence and a Pakistani man was killed amid the tension. In November, hundreds of migrants on the Greek side attacked the Macedonian police with stones amid fears that they might not be allowed to pass.

Over the past few days, the official camp became more orderly, with aid groups running shelters and handing out food and clothing. Still, the flow of refugees had backed up to the Eko gas station, a waiting room for those hoping to continue north.

“We are happy to have made it to Greece, but we want to move on,’’ said Najib Nasrati, 15, who had come from Afghanistan with his family to try to reach Germany.

Earlier in the day, he had heard a rumor going around the Eko parking lot that Germany might completely shut its borders in six months.

“I felt angry when I heard that,’’ he said. “We are all in a very bad situation. If we have to stay in Greece or be sent back, it will be chaos.’’