The Centers for Disease Control and Prevention is considering adding the names of health care workers being monitored for the Ebola virus to the government's no-fly list, federal officials tell Fox News.

The move is being considered as a response to Wednesday's disclosure that Dallas nurse Amber Joy Vinson was cleared to fly on a commercial airliner earlier this week despite having been exposed to the Ebola virus while treating Thomas Edward Duncan at Texas Health Presbyterian Hospital.

Texas health officials announced early Wednesday that Vinson, 29, had tested positive for the virus, making her the second hospital worker to become infected. Vinson's fellow nurse, 26-year-old Nina Pham, tested positive last weekend. More than 70 workers involved in Duncan's treatment are being monitored by the CDC. Duncan died Oct. 8 of the virus after nearly two weeks in the hospital.

On Monday, a CDC official cleared Vinson to fly from Cleveland to Dallas on board Frontier Airlines Flight 1143 despite the fact that she had called and reported having a slight fever, one of the common symptoms of the Ebola virus. Vinson's reported temperature -- 99.5 degrees -- was below the threshold of 100.4 degrees set by the agency and she had no symptoms, according to CDC spokesman David Daigle.

Federal sources, though, are now saying she "lied" about how she was feeling. Though she told the CDC she had a low-grade fever, according to sources her family said she was feeling tired and not feeling well. But sources said this information was not conveyed to CDC officials when she called to ask about flying.

On Wednesday, after Vinson was diagnosed with Ebola, CDC Director Dr. Thomas Frieden acknowledged that the nurse should not have been allowed to board the plane. Vinson had been in Ohio visiting family and had not experienced initial symptoms during her outward journey.

From now on, Frieden said, no one else involved in Duncan's care would be allowed to travel "other than in a controlled environment." He cited guidelines that permit charter flights or travel by car but no public transportation.

Federal health officials are now attempting to track down Vinson's fellow passengers on the flight, the CDC said Wednesday. Frontier has taken the aircraft out of service. The plane was flown Wednesday without passengers from Cleveland to Denver, where the airline said it will undergo a fourth cleaning, including replacement of seat covers, carpeting and air filters. One Central Texas school district temporarily closed three of its campuses because two of its students traveled on the same flight as Vinson.

Early Thursday, Frontier released a statement saying that the crew of Flight 1143 had been placed on paid leave for 21 days, despite CDC guidance that they were all safe to fly. On its website, the CDC says all people possibly exposed to Ebola should restrict their travels -- including by avoiding commercial flights -- for 21 days.

Also Thursday, Texas Health Presbyterian Hospital said it was offering rooms to any workers being monitored for the virus who wished to avoid the possibility of passing the virus to family or friends.

Meanwhile, federal health officials, including Frieden, were scheduled to testify before the oversight subcommittee of the House Energy and Commerce Committee Thursday.

In prepared testimony, Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases at the National Institutes of Health, said Duncan's death and the infections of the two Dallas nurses and a nurse in Spain "intensify our concerns about this global health threat." He said two Ebola vaccine candidates were undergoing a first phase of human clinical testing this fall. But he cautioned that scientists were still in the early stages of understanding how Ebola infection can be treated and prevented.

Medical records provided to The Associated Press by Duncan's family showed Vinson inserted catheters, drew blood and dealt with Duncan's body fluids. Late Wednesday, she arrived in Atlanta to be treated at Emory University Hospital, which has already treated three Americans diagnosed with the virus.

Also Wednesday, President Obama sought to ease fears in the U.S., urging a stepped-up response even as he stressed that the danger in the United States remained a long shot.

"We want a rapid response team, a SWAT team essentially, from the CDC to be on the ground as quickly as possible, hopefully within 24 hours, so that they are taking the local hospital step by step though what needs to be done," he said.

But Obama also noted that the Ebola is not an airborne virus like the flu, and thus is more difficult to transmit.

The president made a point of noting that when he visited with health care workers who had tended to Ebola patients at Emory University Hospital in Atlanta, where Vinson was taken for further treatment late Wednesday, he hugged and kissed them without fear of infection.

"They followed the protocols, they knew what they were doing," he said. "I felt perfectly safe doing so."

Fox News' David Lewkowict and John Roberts and The Associated Press contributed to this report.