Reflecting on his poll numbers in an interview with ABC's Barbara Walters, Obama said: "I've gone up and down pretty much consistently throughout.
"But the good thing about when you're down is that usually you got nowhere to go but up," Obama added, according to excerpts released by ABC.
The interview was taped last week as the Obama administration scrambled to meet a self-imposed November 30 deadline to overhaul HealthCare.gov, the website used in 36 states to shop for insurance under the Affordable Care Act, more commonly known as Obamacare.
Americans trying to use the website have been stymied by errors and slow speeds. The problems meant only 27,000 people were able to use the website to sign up during the first month, and there is now a backlog of Americans to get through the system by a December 23 deadline.
"I continue to believe and (I'm) absolutely convinced that, at the end of the day, people are going to look back at the work we've done to make sure that in this country, you don't go bankrupt when you get sick, that families have that security," Obama told ABC. "That is going be a legacy I am extraordinarily proud of."
Obama officials have said the website should work better for most people by Saturday, although they have warned it will not be perfect.
Before the launch, Obama had assured Americans the website would be as easy to use as Amazon or Kayak, and also promised that people could keep existing insurance plans if they so chose.
But he found himself having to apologize to Americans after falling short on both promises. In the interview Obama said he wants to find out why he was caught by surprise.
"Obviously my most recent concern has been that my website's not working ... and we're evaluating why it is exactly that I didn't know soon enough that (it) wasn't going to work the way it needed to," Obama said. "But my priority now has been to just make sure that it works."
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