ZAATARI CAMP, Jordan—With the Syrian refugee numbers passing the two million mark Tuesday, governments and aid officials are coming to the same reckoning as Mohammad Hariri, an air-conditioner repairman who came here for one night and stayed for a year.

"My opinion is now, on the ground and politically, it's going to take a long, long time," he says.

In early August 2012, Mr. Hariri brought his three children across the border to escape some particularly intense shelling. Today, the camp remains his home—along with some 130,000 other Syrians.

"We used to see refugees on television," says Mr. Hariri, who is also a neighborhood camp leader. "We didn't know what it meant to be one."

The camp, Zaatari, now ranks as Jordan's fourth-largest city, the United Nations says, and as the second-largest refugee camp in the world. Only Dadaab in Kenya, with more than 400,000 people, is bigger, the U.N. estimates.