Switzerland has issued 4,700 special-category visas for Syrians who have family in the country. And Australia, which has come under international criticism for turning away boats of potential refugees from South and Southeast Asia, has said it will take 12,000 from Syria and Iraq.

Germany is in a category of its own, with Syrians making up the largest single group (428,500) of the 1.1 million people who were registered as refugees and asylum seekers there in 2015.

For the United States, as for much of the Western world, the political costs of accepting refugees are high.

Image Refaai Hamo, a Syrian refugee, at a news conference, in Romulus, Mich., last month. Mr. Hamo, who arrived in the United States last month, was among the Obamas’ guests at the State of the Union address on Tuesday. Credit... Carlos Osorio/Associated Press

Many people in the United States are worried about terrorists sneaking in through refugee programs. Crimes like the sexual assaults of women in Germany on New Year’s Eve, in which the authorities said asylum seekers were involved, led Chancellor Angela Merkel to propose tougher laws regulating asylum seekers.

Political figures on both continents have also become openly opposed to accepting Muslims in particular. Donald J. Trump, the Republican presidential candidate, proposed a moratorium on the admission of Muslims to the United States, just as Prime Minister Viktor Orban of Hungary has warned about the need to “keep Europe Christian.”

Perhaps as important, the political rewards for taking in refugees have diminished.

During the Cold War, the West scored political points by welcoming people from the Eastern bloc. It was a way to convey that the Western way of life was better and more attractive than life behind the Iron Curtain. It was one reason, historians say, that in 1980, in the aftermath of the Vietnam War, the United States took in as many as 207,000 refugees, many from Vietnam. In the late 1980s and 1990s, the United States welcomed tens of thousands of people as the Soviet Union was dissolving.