With news of a second confirmed case of Ebola on U.S. soil, questions are mounting over the government's ability to respond to the crisis.

Several Republican lawmakers have called for the Obama administration to name a single point person to make sure the deadly virus doesn't spread.

"I would say that we don't know exactly who's in charge. There has to be some kind of czar," Sen. John McCain, R-Ariz., told CNN over the weekend.

While the White House isn't ruling out naming an "Ebola Czar," they have not done so because their response needs to be "as nimble and as bureaucratically lean as possible in order to bring the overseas epidemic under control and respond efficiently and effectively here at home," according to a National Security Council spokesman.

For now, the White House point person is Lisa Monaco, the president's homeland security and counterterrorism adviser.

"Lisa does have a lot on her plate, but she's a very talented individual," White House Press Secretary Josh Earnest said last week.

The White House stresses that operationally, USAID is in the lead overseas, while, here at home Health and Human Services and the Centers for Disease Control and Prevention are in charge of the preparedness effort. Monaco is tasked with coordinating the interagency response.

In addition to calls for a czar, the ranking Democrat on the House Homeland Security Committee, Rep. Bennie Thompson, wants the CDC to determine whether Ebola patients should be treated at hospitals or moved to biocontainment facilities.

"The CDC attributes the new infection (in Texas) to a breach in protocol, which raises the question whether ordinary hospitals that may not have had specialized training on caring for seriously ill patients safely should be responsible for the long-term care of an Ebola patient when there are beds available in one of our nation's biocontainment units," he said.

The House Energy and Commerce Committee will break its recess to hold a hearing on Ebola on Thursday.

ABC News' John Parkinson contributed to this report