WASHINGTON — Facing sharp questioning at a Congressional hearing on Thursday about the troubled handling of Ebola cases in the United States, federal health officials said that a nurse with Ebola would be transferred to a specialized unit at the National Institutes of Health in Maryland, to ease the burden of the Dallas hospital where she became infected.

Health officials said that the hospital, Texas Health Presbyterian, is strained in its efforts to monitor dozens of other health care workers who may have been exposed to the virus, and that the nurse, Nina Pham, was being transferred at the hospital’s request.

“They are now dealing with at least 50 health care workers who may potentially have been exposed,” Dr. Thomas R. Frieden, the director of the Centers for Disease Control and Prevention, told members of the House Energy and Commerce Committee. “That makes it quite challenging to operate, and we felt it would be more prudent to focus on caring for any patients who come in with symptoms.”

The hearing thrust the deadly virus and the government’s halting management of it into the realm of politics in the midst of a national election season.