As local, state and federal health officials rushed to deal with an Ebola case in Texas, along with the question of whether it could have been spread to other people in the city of Dallas, the response is also a test for the Obama Administration and the President, just over a month before the November mid-term elections.

During a visit in September to the Centers for Disease Control in Atlanta, President Obama not only vowed that U.S. health authorities were ready for Ebola, but that it was rather unlikely that the disease would reach this country.

"I want the American people to know that our experts, here at the CDC and across our government, agree that the chances of an Ebola outbreak here in the United States are extremely low," the President said.

Pressed about that assurance during a briefing for reporters this week, White House Press Secretary Josh Earnest pushed back at any assertions that the Obama Administration had ruled out the chance of Ebola reaching the U.S.

"My suspicion is that you might be slightly over-parsing what the President said," Earnest observed.

Here's part of the longer exchange from Wednesday's White House briefing:

Q - And if I could ask one quick question about the CDC -- because on September 16th the President said, “In the unlikely event that someone with Ebola does reach our shores…” -- he used those words, “unlikely event.” And as we know, there’s a case down in Dallas. Did the President not get, I guess, reliable information from the CDC as to the likelihood that Ebola could come over here? What do you make of that? He talked about it being an unlikely event -- and it did happen.

MR. EARNEST: Yes, would you read that quote for me one more time?

Q He said, “In the unlikely event that someone with Ebola does reach our shores…” I can give you the full quote if you want it. But he talked about it being an unlikely event. He went on to say that the CDC is prepared to deal with that.

MR. EARNEST: My suspicion is that you might be slightly over-parsing what the President said, because when he delivered those remarks there had been at least a couple of health care professionals who had been trying to provide medical services to Ebola victims in Africa who had been returned to the United States for treatment. So obviously these individuals who had contracted Ebola in the performance of their medical work were on the shores of the United States of America.