DALLAS — President Obama raised the possibility on Thursday that he might appoint an “Ebola czar” to manage the government’s response to the deadly virus as anxiety grew over the air travel of an infected nurse.

Schools closed in two states, hospitals and airlines kept employees home from work, and Americans debated how much they should worry about a disease that has captured national attention but has infected two people here.

A federal official said that the Centers for Disease Control and Prevention had broadened its search for contacts of Amber Joy Vinson, the second nurse infected with Ebola at Texas Health Presbyterian Hospital here, after interviewing family members who gave a different version of events from Ms. Vinson’s. The nurse had said she had a slight fever before boarding a flight from Cleveland to Dallas on Monday. But family members said she had appeared remote and unwell during her trip to Ohio over the weekend.

The C.D.C. said it was now tracking down passengers on Frontier Airlines Flight 1142 from Dallas to Cleveland, which Ms. Vinson took last Friday. It had already been tracing passengers on her Monday flight.