NEW HAVEN — The couple from Syria arrived at Kennedy International Airport on Tuesday only to face one more shock in a four-year journey of loss, anxiety and upheaval. They had no idea they had landed in a political maelstrom.

The governor of Indiana, the state that was scheduled to be their new home, had said he would not accept any more Syrian refugees for fear that they might be terrorists. Over the next two days, more than two dozen governors, a majority of the House of Representatives and all of the Republican presidential candidates said they would shut the door to people like them, because American security could not be guaranteed.

“Why did they bring us if they didn’t want us?” said the 33-year-old husband and father, recalling his initial reaction through an Arabic interpreter. “We are coming to an open country.”

“A country with freedoms,” his wife, 23, said.

“We felt rejected,” her husband said. “We were depressed. How could that be the freedoms that we hear about?”