WASHINGTON — President Obama named a trusted political adviser on Friday to take over the government’s response to the deadly Ebola virus, as health officials in two states worked to track a growing list of people who may have been exposed because of missteps in quarantine and containment.

The appointment of Ron Klain, a seasoned Democratic operative and White House veteran, spoke of the seriousness of the situation for the administration, which was eager to put the management of the crisis back on track in the midst of a tough election season. The response has been criticized as sloppy, with two intensive care nurses in a Dallas hospital falling ill after treating a Liberian, Thomas Eric Duncan, who eventually died from the virus. One of the nurses had been allowed to take a commercial flight despite telling the Centers for Disease Control and Prevention that she had a slight fever.

The appointment came a day after members of Congress lashed out at federal health officials and just hours after the disclosure by the State Department that yet another employee of the Dallas hospital, Texas Health Presbyterian, who had handled Ebola specimens in a lab, had traveled, boarding a Caribbean cruise ship. The government of Belize said the ship was in that country’s waters, but the authorities there have refused to allow American officials to evacuate the passenger. Mexico would not even allow the ship to dock, and it was headed back to Galveston, Tex., with the lab worker held in isolation. Officials said the risk of infection was very low, but the revelation deepened the impression that the administration was struggling to stay ahead of the virus and the public anxiety.